Are we allowed to use sound effects from other NES games, or do they have to be completely original?

This jam doesn't explicitly mention it, but most jams say you can use anything that you legally have the right to use -- which means no sounds directly from existing, copyrighted games. If you do make a "fan game" that uses graphics, sounds, or characters from an existing NES games, you're in a legal gray area. Likely it'll be fine, but you do open yourself to Nintendo and other copyright holders complaining via a DMCA request, and taking your game down.

besides the copyright infringement issue that Morph mentioned above, this jam does explicitly mention:

“All assets must be created during the jam.”

so, no. you can’t use sound effects from other games. they have to be made by you during the jam.