Meaning conscious / sentient / intelligent entities from elsewhere in our Universe.
Legal Rights of ETs by Robert Freitas, author of Xenology. He goes through a lot of legal categories that they could fall into, and he seems to think that "stateless persons" is the best fit.
The Space Review: Legal implications of an encounter with extraterrestrial intelligence by Babak Shakouri Hassanabadi.
He concludes that "The best approach would be to assign the aliens the same legal rights that foreign diplomats enjoy while they are on mission in foreign countries."
BSH also concludes that the appropriate organization to negotiate with ET's is the United Nations -- it's the closest thing to a political organization that represents all of humanity.
-
Now for the question of the legal status of the activities of ET's. This issue will require a lot of introduction, because similar issues have long been an issue among us Earthlings, with varying degrees of legal resolution. We must first start with the locales of their activities. 
International waters has a nice diagram of which areas have which statuses.
Complete sovereignty: a government regulates both passage and economic activities. Land surface, land underground, continental-shelf underground, internal waters, territorial waters, national airspace.
Partial sovereignty: a government regulates economic activities, but allows unregulated passage. Continental-shelf surface, extended continental shelf, exclusive-economic-zone waters, territorial-waters airspace.
No sovereignty: no government regulation of either passage or economic activities. Ocean floor, international waters, international airspace, outer space.
"Waters" includes both water surface and underwater volume. "Passage" is traveling through and stopping if necessary or desired.
air law | Britannica.com
Quote:
It follows from the principle of airspace sovereignty that every state is entitled to regulate the entry of foreign aircraft into its territory and that persons within its territory are subject to its laws. States normally permit foreign private (i.e., nongovernmental and noncommercial) aircraft to visit or fly through their territory without too much difficulty. Such aircraft registered in states that are parties to the 1944 Chicago Convention are, under the convention, allowed into the territories of all other contracting states without prior diplomatic permission if not engaged in the carriage of passengers, mail, or cargo for reward.
As to the boundary between airspace and outer space, that is often taken to be the von Karman line, where a typical airplane must fly at orbital speed in order to get enough lift. That is approximately at 100 km / 60 mi above sea level.
So if ET's stay above the von Karman line, they don't have to tell us about their travels, let alone request permission, as long as they don't do anything troublesome, like make lots of radio noise or try to bring aboard an active spacecraft without permission.
If they travel in our planet's atmosphere, then they'd fall under the laws that govern our aircraft. Over land and internal waters, they'd be traveling in some nation's sovereign airspace, subject to the approval of that nation. I myself believe that there is no convincing case of any UFO being an extraterrestrial spacecraft or something similar, but it's interesting to consider how that hypothesis works out in this context.
Most UFO's are distant lights or other distant objects, and most UFO's do not do hostile activity, unless one counts trespassing in national airspace or restricted airspace. So their presence may be considered tolerable, and it is not surprising that the US Air Force stopped investigating UFO's in 1969 because there was no evidence that they are a threat to US national security.
However, a few UFO's have (seemingly) done hostile things, most notably Thomas Mantell's UFO. According to some UFO believers, that UFO attacked his plane, and that's what made it go into a dive and crash. But even then, it could have been an accident, as George Adamski claimed in Inside the Spaceships. He claimed that one of his ET friends told him that when he was riding in one of his ET friends' spaceships. ST:TOS episode "Tomorrow is Yesterday" has a very similar scenario, with the USS Enterprise as a time traveler that became a UFO and that inadvertently destroyed a military airplane, though with rescuing its pilot. The rarity of hostile actions by UFO's would seem to support the accident theory.
So one can use appropriate liability law for (say) ship or airplane collisions. However, the Mantell incident was a hit-and-run incident, and that may cause complications.
Now for other purported ET activities.
Crop circles and domestic-animal mutilations: Vandalism. Deliberate damage or destruction of others' property without their permission.
Abductions: Very antisocial, and a serious crime. A lot of abduction-related activities seem like what a wildlife biologist would do, and that would make the abductors violate common human-experimentation protocols.
Friendly contacts: What George Adamski and other UFO contactees had claimed. No problems there in general. It's worth noting an urban legend about such contacts. snopes.com: Extraterrestrial Contact Law: "A federal law prohibits U.S. citizens from having contact with extraterrestrial beings." That's a misunderstanding of the Extra-Terrestrial Exposure Law, where visitors to other celestial bodies are to be be quarantined. The Apollo 11, 12, 13, and 14 astronauts were quarantined, but the Apollo 15, 16, and 17 ones weren't. So there is no law against such contacts.
Covert residence: George Adamski and some other UFO contactees have claimed that some of their ET friends reside among us, almost indistinguishable from us, complete with false identity documents. They'd be illegal aliens in two senses, foreigners and ET's, and they would be guilty of participating in identity fraud.
Bases: Some people claim that Mt. Shasta and various other mountains are UFO/ET bases. Surface and underground bases would be in some nation's territory except for such bases in the ocean floor or in Antarctica.