How does President Trump's travel ban affect nationals of Iran, Iraq, Libya, Somalia, Sudan, Syria or Yemen coming to the US for tourism/transit/etc?

A message I received from my university three hours ago (2017-01-29, 6 PM UTC) seems to indicate that in Massachusetts the ban is lifted for the next seven days:

Early this morning, the Massachusetts federal district court issued a temporary order that restrains the government from enforcing the Executive Order to detain or remove holders of a valid visa or green card who travel from the seven countries to the US through Logan Airport. This order is in effect for the next 7 days. The seven affected countries are: Iran, Iraq, Libya, Somalia, Sudan, Syria, and Yemen. […] We encourage you to fly back to Boston–directly to Logan Airport–as as soon as possible, and before February 4.

Update on 2017-02-03:

Two MIT undergraduates who were denied re-entry to the United States
last weekend landed at Logan Airport on Friday afternoon. The students
are now back on campus. Both were prevented from boarding flights back
to Boston last weekend after spending the winter break with their
families.

The two undergraduates’ return to the U.S. was made possible by a
temporary order issued by the Massachusetts federal district court
last weekend, restraining the government from enforcing the executive
order to detain holders of valid visas or green cards who travel from
the seven affected countries to the U.S. through Logan Airport.

On Thursday, an airline announced that it would begin allowing
passengers affected by the executive order to board international
flights bound for Logan. MIT officials moved quickly to get the two
students — with whom they had been in regular touch — onto one of this
airline’s flights back to Boston.

Update – November 2017

On the 13th of November, the preliminary injunction (which prohibited the US government to enforce the presidential proclamation) was stayed except for foreign nationals who have a credible bonafide relationship with someone in the US.

A summary of the subject countries is:

So nationals of Chad, Iran, Libya, Somalia, Syria, and Yemen will remain travel restricted to the US unless they have a parent, including parent-in-law, spouse, fiancé, child, adult son or daughter, son-in-law, daughter-in-law, sibling, brother-in-law, sister-in-law, grandparent, grandchild, aunt, uncle, niece, nephew, and first-cousin. For all relationships, half or step status is included (e.g., “half-brother” or “step-sister”) in the US. Any other extended family members will not count as a bonafide relation.

Situation as of Saturday 4 February, 2017

A federal judge has rules the ban is unlawful/unconstitutional and until further notice, the ban is on hold. This means any national of the aforementioned countries, with a visa or green card, can currently travel to the USA. This might change any moment if a higher court rules differently, so if you live in the USA (like with a student or J-1 visa), you should travel ASAP.

Situation as of Saturday 28 January, 2017

The ban includes both immigrant visas, nonimmigrant visas, and green card holders. From the executive order (emphasis mine):

I hereby proclaim that the immigrant
and nonimmigrant entry into the United States of aliens from countries referred to in section
217(a)(12) of the INA, 8 U.S.C. 1187(a)(12), would be detrimental to the interests of the United
States, and I hereby suspend entry into the United States, as immigrants and nonimmigrants, of
such persons for 90 days from the date of this order (excluding those foreign nationals
traveling on diplomatic visas, North Atlantic Treaty Organization visas, C-2 visas for travel to the
United Nations, and G-1, G-2, G-3, and G-4 visas).

According to Reuters, a Department of Homeland Security (DHS) spokesperson said greencard holders are included as well:

People holding so-called green cards, making them legal permanent U.S. residents, are included in President Donald Trump’s executive action temporarily barring people from seven Muslim-majority countries from entering the United States, a Department of Homeland security spokeswoman said on Saturday.

There is ongoing confusion concerning people with dual nationality, such as people holding both UK and Iranian passports. (However, dual nationals who also hold US citizenship are OK, since US citizens cannot be denied entry to the US.)

The only currently stated exceptions are holders for the aforementioned visa categories, which essentially means diplomats, UN personnel, or NATO staff:

• C-2 visas, officially for people visiting or working at the UN headquarters, but rarely used (according to phoog)
• G-1 visas for designated principal resident representatives of foreign governments and their family,
• G-2 and G-3 visas, which are very similar to G-1 visas,
• G-4 and NATO visas

Late Saturday

A federal court, responding to a lawsuit filed on behalf of detained travelers, has issued an emergency stay quashing part of the order for the time being. It forbids the US Government from

removing individuals with refugee applications approved by U.S. Citizenship and Immigration Services as part of the U.S. Refugee Admissions Program, holders of valid immigrant and non-immigrant visas, and other individuals from Iraq, Syria, Iran, Sudan, Libya, Somalia, and Yemen legally authorized to enter the United States.

This does not say that the persons concerned have to be let into the United States, only that they can’t be sent back. It is possible they will stay in limbo at the airports until the legal situation clears up further.

It is also not clear if airlines will now allow such persons with already issued visas to board flights to the US.

Update: Sunday January 29, 2017

Airlines have started to refuse boarding to those holding valid visas from those countries that are on the temporary ban list; and some passengers have been stopped at transit points.

Five Iraqis and a Yemeni national were kept from boarding a flight
from Cairo to New York on Saturday, despite all seven people having
already obtained the necessary migration visas to enter the United
States.

Source: DW

In The Netherlands, the Dutch flag carrier KLM said it had stopped
seven passengers from boarding its flights, five of whom it had been
able to contact before departure. The identities of the seven, their
countries of origin and destinations were not given.

"We would have liked to have had them fly with us, but it would not
have made much sense because they would have been denied entry" to the
United States, KLM spokesman Manel Vrijenhoek told AFP news agency.

In Canada, WestJet Airlines said it turned back a passenger bound for
the United States on Saturday in order to comply with an executive
order that prohibits people from seven Muslim-majority countries from
entering the United States.

WestJet spokeswoman Lauren Stewart said the airline would give full
refunds to anyone affected by the US executive order. It did not say
which country the passenger had come from.

Source Al Jazeera

Sunday January 29, 2017

British Conservative Member for Parliament Nadhim Zahawi is now unable to visit his sons who are at Princeton University. He represents Stratford on Avon, The birthplace of William Shakespeare. Zahawi is a British Citizen who was born in Iraq under the rule of Saddam Hussein, from which his Kurdish family fled in 1976 when Zahawi was aged 9.

Source: BBC

The US State Department said that Britons with dual nationality with Syria, Iraq, Iran, Sudan, Libya, Somalia and Yemen will be stopped at the US border for the next 90 days.

Source: The Telegraph

British Foreign Secretary Boris Johnson held conversations with the US government on Sunday.

The Foreign Office then advised British travelers that dual citizens were only affected if traveling to the US from one of the seven banned countries.

Source: BBC

Omid Nouripour, a Green Party MP with German-Iranian citizenship, is reported to be one of ten thousands of German citizens believed to be banned from entering the US under new rules. Nouripour is the vice chair of the German parliament’s American-German group and a member of the steering committee of Germany’s Atlantic Bridge programme.

Source: SPIEGEL,WELT

Canadian dual citizens might be exempt as long as they travel on their Canadian passport, though whether US immigration will make that distinction in the current uncertainty remains to be seen.

Source: Government of Canada, Canadian Prime Minister’s tweet

U.S. Customs and Border Protection (CBP) has briefed the global trade group that passport-holders from states such as Iran and Iraq, including cabin crew, will be barred entry to the United States, IATA said in an email to its member airlines, seen by Reuters.

Source: Reuters