So Santa Claus lives at the North Pole (which we'll naturally assume is at the exact location of the Earth's north pole). If someone wanted to, for instance, sue Santa for IP infringement or arrest him for his multiple felonies, would his home at the North Pole be under the legal jurisdiction of any country?
First off, the people of Finland say that Santa lives in Korvatunturi, which would mean he is subject to Finnish jurisdiction.
But if he were born, resided and worked at the North Pole, as the original question states, this spot is in international waters, and under the Convention on the High Seas that would be terra nullius. Therefore no nation can claim sovereignty over his home (we must also assume he is not on a plane or ship flying the flag of some nation: article 11 allows the detention of a ship on the high seas only under order of authorities of the flag state). That might immunize him from civil forfeiture of his home, but there is more to jurisdiction than where your home is.
Under Article 14, all states "shall co-operate to the fullest possible extent in the repression of piracy on the high seas or in any other place outside the jurisdiction of any State". Article 15 says what "piracy" is, which could be interpreted as referring to crimes against persons and property (but not possession of marijuana). Eritrea is not a signatory to this treaty, so they might claim legal jurisdiction, though enforcement of the claim could be challenging. The US has technically not ratified this treaty either, but we mostly observe it.
Klaus could also be subject to US law (for example) in specific cases. The high seas are in the "special maritime jurisdiction" and the US can claim jurisdiction for offenses against a national of the US. Other states may have similar laws.
A person whose IP had been copied can sue in their home country, so the lack of a North Pole jurisdiction would not protect Claus.
B&E is prosecuted where the offense happens; he would be free of business license laws; when he enters US airspace, he is subject to FAA regulations, and would be required to have a visa and passport to enter the US. In fact, most of the alleged crimes take place within the jurisdiction of a state.
@User6726 has some useful info on various jurisdictions, I felt it necessary to include some remarks about Santa's citizenship status.
Santa Claus would be an alias of Saint Nicholas of Myra. He was born in Demre, Turkey, on March 15, 270 AD. This would most likely make him a citizen of modern Turkey, the legit modern government of the country. Turkey does allow dual citizenship though no specific claims with regards to Santa's current status.
Santa's residence is traditionally Magnetic North Pole and on land. This was first described by American Cartoonist Thomas Nest in 1879. Nest provided a series of paintings that were the first known depictions of Santa's home and workshop on solid land and under the Aura Borialis. At the time, Magnetic North was under the Canadian Arctic Archipelago, most likely Somerset Island, given historical pole locations. In 2008, Santa Claus was granted Canadian Citizenship by then Minister of Citizenship, Jason Kenney. Prime Minister Justin Trudeau (then Parliamentary secretary to Prime Minister Stephen Harper) announced that "Everyone knows Santa Claus is Canadian". The Canadian postal code system lists Santa's postal code as HOH OHO.
This presents a problem for Nordic Citizenship claims, as most of those countries would not have recognized Dual Citizenship prior to the 2000s, though nearly all of them maintain Santa has residence in their country. It could be possible that Santa is a resident, but not a citizen, and maintains residencies and mailing addresses in these countries as vacations or possible alternative production sites or distribution centers. They could also be used to relieve the stressed Canadian postal system, which requires 11 thousand volunteers to assist in the estimated one million letters addressed to Santa (many from outside the country) each year. These include Drobak (Norway), Uummannaq (Greenland, Denmark), Mora (Sweden), and Belovezhskaya Pushcha National Park (Belarus). Santa also has a residence in the United States in the town of (surprise surprise) North Pole, Alaska.
Much of Santa's actions during Christmas may be ignored by under proprietorial discretion. As seen in "Kringle vs. The State of New York" as depicted in the film "Miracle on 34th Street" Santa's status as a nearly universally beloved figure can be fraught with all sorts of political issues a typical case would ordinarily not worry about. With reguards to Breaking and Entering Charges, a skilled defense lawyer would easily argue that Santa is not in fact an welcomed visitor and therefor his entry would be lawful. This is further backed that by leaving a form of per-arranged payment (milk and cookies, possibly provisions for reindeer in the form of apples or carrots), Santa's entry was lawful as he was invited into the private residence.
In the United States, NORAD (U.S.-Canada joint airforce program) does track Santa's trip across the world, presumably to assist in flight clearance with other nations. Updates on Santa's journey are available for public information in a timely format.
Santa is likely a Turkish Citizen by birth with dual citizenship in Canada, and resides in the Canadian Arctic Archipelago. Santa has mulitple residences in other nations, most with significant territory claims above the Artic Circle in Europe and North America, but is likely not a citizen of these countries as they have strict laws regarding dual citizenship. Santa would typically fall under Canadian jurisdiction for all crimes, though any prosecutorial effort would most likely be a politically negative move for the office that seeks legal actions against Santa.
the tricky thing here is going to be perfecting service. As Santa Claus clearly does business everywhere he can be subject to the jurisdiction of everywhere he goes. In Kansas, for instance, suits have to be filed in a county where the defendant can be served. Based on Santa's famous knowledge of the sleep/awake and naughty/nice statuses of all persons, it seems that finding a licensed process server not only able, but also willing, to serve papers on Santa Claus "as he flys by" would be insurmountable.