Some places, like embassies and military bases, are considered US soil, even if not traditional. Can one operate with a US call sign in such situations, and how should it be done?
I can find no indication that a US-issued amateur licensed would in itself grant you the right to operate on such fringe places. §97.5 (a) reads:
(a) The station apparatus must be under the physical control of a person named in an amateur station license grant on the ULS consolidated license database or a person authorized for alien reciprocal operation by §97.107 of this part, before the station may transmit on any amateur service frequency from any place that is:
(1) Within 50 km of the Earth's surface and at a place where the amateur service is regulated by the FCC;
(2) Within 50 km of the Earth's surface and aboard any vessel or craft that is documented or registered in the United States; or
(3) More than 50 km above the Earth's surface aboard any craft that is documented or registered in the United States.
An embassy is not 50 km above the Earth's surface, nor is it a vessel or craft. So the question then becomes: is an embassy a place where the amateur service is regulated by the FCC?
This is a bit tricker to answer. The FCC's web page "What We Do" reads:
The Federal Communications Commission regulates interstate and international communications by radio, television, wire, satellite and cable in all 50 states, the District of Columbia and U.S. territories.
Now, I am by no means an expert in international law, but I'm guessing that even if the US does exercise extraterritoriality in the case of embassies and whatnot, they are not claimed as US territories per se, and the US is not going to jeopardize its diplomatic relationships by letting some ham set up a high power station that disrupts local communications. Likewise military bases are not keen to attract negative attention, and commanding officers don't require a law to justify making your life miserable. In either case, you will probably be asked, then made by force to stop or leave, regardless of how vehemently you argue with the authorities.
Fortunately, there are plenty of places that have signed reciprocal agreements with the US which would permit one to operate in a foreign country ordinarily. If your goal is radio operation, and not a legal challenge, this is the way to go.