I'm playing on a multiplayer server with origins and stuff, I crafted two Diamond Longswords but they don't work.
I'm on 1.17.1

Yeah, I'm unable to hit entities with them, single-wield or dual-wield.

What do you mean by "they don't work" exactly? you can't hit entities with them?

If you can't even swing the sword, it's probably because you have something in the other hand(shield, totem, etc.), if it still doesn't work, well, I can't help you

My guess is, as KubanczkT said, you had another item in your other hand while trying to use such big weapon. Reopen if that is not the case