To deny something is to say something is not true, or say that you DID NOT do something:
To refuse is NOT to do something, or to say firmly that you WILL NOT do something:
Note that after deny we use the -ing form or a noun, and after refuse we use the “to” form of the verb.
To reject something is to not accept it – often because it’s not good enough, or because you don’t believe in it.
To decline is to say “no” politely to a proposal, invitation, or suggestion