Can we meaningfully compare the poverty levels in the USSR to those in the USA at the same time and to those in the USA today?

You could always find statistics where USSR looked better

There are three kinds of lies: lies, damned lies, and statistics. If you want to find the "proof" that life in USSR was better than in US (at least for the poor), there are metrics that could help you.

Unemployment in USSR was very low, officially 1-2%, far lower then US unemployment which never got below 2% and most of the time was above 4%. In practice, this meant that almost everybody capable for work was assigned some position, i.e. some job. Was that position economically really profitable and necessary is debatable. Soviet enterprises were chronically overstaffed and inefficient. As a result, wages were comparatively low . From late 1950's they would provide for basic necessities like food and some clothing, but not much else . We pretend to work, and they pretend to pay. Comparatively, workers in US would have less job security, but they would enjoy higher wages, could earn more if they specialized (in USSR this was not always the case) and they could start their own enterprises.

Also, officially homelessness in USSR didn't exist, unlike US . Everyone had to have place of residence, not having it was considered a crime. Unofficially, homeless did exist in USSR, although on a much lower scale then in US. What is more important is that average housing in USSR was much worse then in US, with multiple families sharing one flat. Also, practically all housing in cities was state owned, it was difficult to move and almost impossible to own your own residence. Again, vastly different from Western system where you would have a chance to work for and earn your own house.

Finally, in theory Soviet health care was universal and available to all. In practice, average Soviet hospital lacked much of equipment available in the West. There were of course special hospitals with better equipment and better medical staff but they were available only to Party nomenklatura and occasionally to those able to bribe their way in and be treated by "professors" . Of course, we could argue that health care system in US favors the rich, but overall, opportunity to earn for better treatment was much bigger in US, hence longer life expectancy.

Overall as a conclusion, USSR as a socialist country tended to suppress extreme poverty, but average Soviet citizen lived much worse then average US citizen.

I will argue that 'poverty' in modern societies is more of a social construct rather than an objective reality. Roughly speaking, people at the 'bottom' of society will feel poor, even if they have more disposable income than an average person in another country.

There is an objective 'extreme poverty' end of it, on the level of 'who of my children will eat today', but this practically didn't exist in the USSR since at least late 50s. (I'll be talking about these times, 1960s+).

In this social sense we probably can make some comparison, but it will necessarily lack the air of 'objectivity' that comparing 'dollars' (or burgers) may give. In addition, the essential absence of social sciences in the USSR (and hence the lack of fair opinion surveys) will require us to make conjecture from secondary information and experience.

Since there was no market per se in the USSR, the prices did not reflect the utility or demand of the product. As a consequence, the level of personal income didn't matter as much as it does in a market economy. Hence any monetary comparisons are meaningless. An income of (say) 200 roubles doesn't mean much if you can't use it to buy what you want, despite low prices. On the other hand, with (almost) free accomodation, medicine and education, and cheap and available most basic necessities such as bread and milk, one could get by with only casual income of ~2 roubles/day and even less (or even by recycling abandonned glass bottles).

Now, were these people who lived in shared apartments and collected bottles on the streets poor? By most objective measures, probably yes. But did they think of themselves as poor? I'd say no, en masse.

First, such behaviour was very common and was not stigmatised. Living in an apartment block of public housing may be a sign of poverty in the US, but a norm or even rather a privilege in the USSR, so nobody felt disadvantaged by it.

Second, the Soviet society was generally not structured by wealth. Contrary to popular myth, it was a very hierarchical society, but in non-economic (or rather, non-financial) terms. It was structured by access to privileges. A shop assistant or a butcher were not (officially) highly-paid occupations, but they had direct access to sought-after goods, and so were considered relatively privileged. A factory director or a general might get double or triple of an average worker, but their main advantage was access to special shops where they could actually spend these money.

In other words, people were not divided into 'rich' and 'poor' (at least, they did not feel that way), but rather into 'privileged' and 'unprivileged'. Most people made their way in life not so much through career in a proper sense, but through making as many connections with 'privileged' people as possible.

Thus, if we think of 'powerty' in this sense, we'll likely find that a lot more people in the US were considered (and considered themselves) as poor (below 'poverty line', whatever it means), than in the USSR.

Question:
Can we compare meaningfully the poverty levels in the former USSR to those in the USA at the same time and to those in the USA today?

Short Answer:

The Soviet Union did not permit outside or objective reporting of embarrassing facts throughout its history. It mostly denied the existence of poverty in their system entirely, claiming poverty was a Western evil of capitalism. Towards the end of the Soviet Union days it pursued a policy of openness and reform; this resulted in the first glimpses of the Soviet's internal numbers of systemic poverty. They showed in 1989 the Soviet Union had systemic 20% of it's population below the poverty line. The article quotes Leonid E. Kunelsky, chief of the economics department at the State Committee on Labor and Social Issues, who's Soviet Poverty numbers double that of the official estimate. The poverty level in the United States at the same time was 14%.

Detailed Answer:

During Michael Gorbachev's glasnost(openness) and perestroika (reform) campaigns the west got it's first hard numbers on poverty levels in the soviet union. Up to that point the Soviets always represented poverty as a western capitalistic problem and denied it's existence within their borders.

In 1989 the communist newspaper Pravda published an article on internal Soviet numbers picked up by the New York Times.

New York Times Jan. 29, 1989

Soviet Openness Brings Poverty Out of the Shadows

But the Soviet authorities, who once denied that poverty existed in their country and pronounced it an evil of capitalism, now say that tens of millions of Soviet citizens - at least 20 percent of the population - live in poverty, compared with about 14 percent in the United States. 'Our National Tragedy' .

Their condition has drawn a remarkable amount of attention in the Soviet press in the last year, with frequent letters from poor people bemoaning their misfortune and articles by economists and sociologists blaming the Government for neglecting the problem.
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''Poverty is a reality, our national tragedy,'' the newspaper Komsomolskaya Pravda recently wrote.
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Officially, the poverty level in the Soviet Union for an urban family of four is 205.6 rubles a month ($339.24 at the officially established exchange rate of $1.65 to the ruble). This is about 51 rubles or $85 a person(/month). .

But the Soviet authorities and academics readily admit that the figure, calculated in the 1960's, is outdated. Most agree that around 75 rubles, or $124, a month a person are necessary for what the Government calls ''minimum material security.'' No Plan for Poverty
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Between four and five million Soviet families fall below the formal poverty level, according to Soviet officials, and a full 20 percent of the population lives on less than 75 rubles a month.
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''More than 43 million people are living in families with incomes of less than 75 rubles a month per person,'' Leonid E. Kunelsky, chief of the economics department at the State Committee on Labor and Social Issues, said. ''We have to do something to help these people.''
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There is no state plan, however, for dealing with poverty, according to interviews with several Soviet officials.

It is very difficult or impossible to compare. By some standards almost all Soviet citizens were poor. By other standards they were OK.

There is no adequate conversion rate of the Soviet rouble. Prices in roubles were not true market prices: most of them were arbitrarily established by the state. Many things were cheap but not easily available. Let me compare the things which make major expenses in the US:

• Housing. There was very cheap housing available from the state for rent. The problem was that it was not really available to all: there was a shortage. One had to enroll to a waiting list, and stay in this list for years. How many years, depended on the city, your place of work etc. Many people lived for decades in dormitories or with their parents.

• University education was free (I mean no tuition, but you had to pay for your living, books etc.) Enrollment was (theoretically) merit based. Those who had good grades obtained a stipend, and free or extremely cheap dormitory accommodation. So if you are a A-B student, you get a stipend and a dormitory, and in principle you can survive without spending any extra money, on a minimum survival level. Elementary education was free and mandatory.

• Medicine. Medicine was free. (One can discuss its quality, availability, etc. but it was free). However, as it happens with most things which are free but in shortage, you may have to pay (illegal) bribes to obtain the service.

• Employment. Officially, there was no unemployment. University graduates were assigned jobs. One had to work 3 years on the assigned job, and then you could change it if you wish. Finding a job as a laborer was never a problem. Moreover, if you live in a city and have no job, you could be deported by a court decision as a "parasite". An occupation as housewife was legitimate but rare: usually one salary was not enough to support a family.

• Retirement. If you worked certain number of years, you automatically qualified for state retirement. Also in the case of disability. This can be compared to Social security in the US. If you rent an apartment from the state, you could survive on your retirement money, which would be spent only on food.

• Vacation. Some payed vacation (from 2 weeks to 2 months per year, depending on your job) was guaranteed Cheap or free vacation packages were distributed by employers, as a "reward for good work". You could also travel on your own.

So a very large portion of expenses of a typical family was food and clothes.

Cars were considered a luxury, they were expensive AND they were in shortage. (One also had to be on a waiting list, as for an apartment, for many years). But, on the other hand, it was relatively comfortable to live without a car: public transportation was well developed and very cheap.

So how can one compare?

I can give some numbers from my own experience (early 1970s). Working as a laborer (with no qualification) I could make 100-120r per month. A laborer of high skill could make 200 and more. Apartment rented from the state was 10-20r, but a private apartment rental 100-200. As a student, I obtained 35-45r as a stipend, this was barely enough for good food, but my fellow students saved on food. I did not qualify (and did not want to) live in a dormitory because my parents were considered "highly paid", and this was considered in dormitory distribution (as I said EVERYTHING was in shortage). "Highly paid" meant at that time 400-500 roubles/month. My parents rented an apartment from the state, the rent was 10-15 roubles, perhaps 30 with utilities. They had no car, and no real need in it. A ride in a bus/trolley/tram/subway was 3-5 kopeks (1 k=1/100 of a rouble). Bread was 20 kopeks/kilogram.

Most people in the cities rented apartments but one could also buy a house, for a price like 10,000-20,000 or more (about 100 monthly salaries of a worker).

A soft cover book was less than 1 rouble, hard cover 1-2 roubles. Relatively cheap poor quality cloth was available, but genuine US made jeans could be 100-200 roubles (sold illegally) and some of my fellow students starved to save for this luxury item:-)

When I came to the US in the late 80s my "rule of thumb" conversion rate for daily necessities was 1 rouble = $10.

There was such thing as the "minimal wage" which slowly increased from about 30 roubles/month in 1960 to about 100 r in the 1980s.

Officially, there was no inflation: the price of bread did not change at all in the period 1960-1980. And I remember only one year when bread was in some shortage (in the middle 60s). As I said, the prices were established by the state, and changes were posted in newspapers and broadcast on the radio. They maintained that price increases were only for "luxury items".