The CDC's pages are the best source for this. Below are the answers to your questions as of December 10, 2021.
You are not required to present a negative test result at the land border or when arriving by sea. From the FAQ on this page (scroll down):
Does this Order apply to land border crossings or persons arriving at seaports?
No, the requirements of this Order only apply to air travel into the U.S.
You are required to provide a negative test taken within the past 24 hours if you arriving by private plane. See this guidance for aircraft operators & airlines:
Does this order apply to all flights or just commercial flights?
This order applies to all flights, including private flights and general or business aviation aircraft (charter flights). Passengers two years of age or older traveling by air into the United States are required to present a negative test result or documentation of recovery regardless of flight type.
The consequences for an aircraft operator that does not check test status, or for an aircraft passenger that does not provide test status, are laid out in the official CDC order (as revised 2021-12-02):
Any airline or other aircraft operator that fails to comply with [these requirements] may be subject to criminal penalties under, inter alia, 42 USC 271 and 42 CFR 71.2, in conjunction with 18 USC 3559 and 3571. ...
Any passenger who fails to comply with [these requirements] may be subject to criminal penalties under, inter alia, 42 USC 271 and 42 CFR 71.2, in conjunction with 18 USC 3559 and 3571. Willfully giving false or misleading information to the government may result in criminal penalties under, inter alia, 18 USC 1001.
From this description, it sounds like you wouldn't be prevented from entering the United States on a private plane without a negative COVID-19 test, but you and/or your pilot might well be taken into custody for violating federal law.