Can H1 visa holder enter sweepstakes and contests? And are H1 visa holders considered legal US residents?

Yes, you may enter sweepstakes. You should look at the rules of any sweepstakes, e.g. Publisher's Clearinghouse, to see how they define "resident."

It depends on the rules of the sweepstakes and how they define legal U.S. residents.

For immigration purposes, H1B holders are considered "legally" in the country bur not lawful permanent residents or as you call them US legal residents. Although you reside in the US and are legally here, you should be careful when you classify yourself as a us legal resident because these are terms of art and have very specific definitions.

An H1 visa does not give "residence". This doesn't mean you can't enter in a contest, unless the rules specifically state you must me a legal resident.

Aneliya laid it out perfectly www.Immigration-Lawyer-NJ.com