Devas and Asura?

Yes a human can get rebirth(given that has not attained nirvana, or still has greed, aversion and delusion) in one of the four hells, in the human world, in one of the six heavens or in planes of forms or planes of formless. 16 planes of forms and 4 planes of formless. Altogether there are 31 places a human gets rebirth. Actually Asura term is ambiguous, it may mean one of four hells or devas in the tawtisa heaven. You can read in detail about the 31 planes in this book. Ten meritorious actions and avoiding ten evil acts and good thoughts at the moment of death can give a rebirth as a Deva.
www.bps.lk/olib/wh/wh462.pdf
Yes devas can get rebirth in any of the 31 planes including human or heaven. But I do not think any of Buddhist texts tell a case where a Deva gets rebirth as a Deva forever because the thought at the moment of death really matters in determining the next birth. An unwholesome thought can give a bad rebirth and it is not unlikely to happen. Yes right path or kusal can give a human the rebirth in the heaven. But there is a lot of detail behind that. And I am not sure whether a being in a hell can get rebirth as a Deva when it is extremely difficult to get a human rebirth. You can read more on Karma in this article.

http://www.buddhanet.net/e-learning/karma.htm

Great question!

The short answer according to Buddhism is yes, you can be reborn in those realms.

However, there is a reason Saṃsāra is refereed to as "cyclic existence"; Because the cycle through these realms is like a spin cycle where you are thrown from realm to realm, life to life, with little control over which realm you land in, at least without some understanding of karma.

While shooting to be reborn in these rhealms will bring a life or two of comfert, and following the advices user5380 laid out will get the result. These realms though, like everything else in Buddhism, are impermanent

In those realms you are burning through large amounts of positive karma, while creating very little if any, good karma.

In Buddhism, rebirth in the human realm is considered to be a better outcome, and preferable.

Can a human through the right path be reborn a Deva or Asura?

Devas are reborn in the sensuous planes I will explain what you must develop to be reborn there. Those who are reborn in the Sensuous places would have to develop virtue:

Then there is the case where a certain person refrains from taking life, refrains from taking what is not given, refrains from sensual misconduct, refrains from false speech, refrains from divisive speech, refrains from abusive speech, refrains from idle chatter, is not covetous, bears no ill will, and has right views. With the break-up of the body, after death, he reappears in the company of the devas. He lives there, he remains there, by means of whatever is the food of devas. This, too, is an impossible place for that gift to accrue to one staying there. (AN 10.177)

They must develop generosity as well:

Then there is the case where a certain person refrains from taking life... and has right views. And he gives food, drink, cloth, vehicles, garlands, scents, creams, bed, lodging, & lamps to brahmans & contemplatives. With the break-up of the body, after death, he reappears in the company of devas. There he experiences the five strings of divine sensuality [delightful sights, sounds, smells, tastes, tactile sensations]. It's because he refrained from taking what is not given... and had right views that he reappears in the company of devas. And it's because he gave food, drink, cloth, vehicles, garlands, scents, creams, bed, lodging, & lamps to brahmans & contemplatives that he experiences the five strings of divine sensuality. But at any rate, brahman, the donor does not go without reward." (AN 10.177)

I do not see being born as an asura is a good thing. For they are overcome by wrath, jealousy, and envy.

From my understanding, they can drop and be reborn in the human destination. I'm not certain which sutta says that.

Here is more info on the 31 Planes of Existence