Definitions from TFD:
Refuse: To indicate unwillingness to do, accept, give, or allow
Reject: To refuse to accept, submit to, believe, or make use of.
Decline: To express polite refusal.
They are all synonyms. But the difference between them is more clearly depicted here under synonyms:
Synonyms: refuse, decline, reject, spurn, rebuff
These verbs all mean to be unwilling to accept, consider, or receive someone or something.
Refuse usually implies determination and often brusqueness: "The commander . . . refused to discuss questions of right" (George Bancroft). "I'll make him an offer he can't refuse" (Mario Puzo).
To decline is to refuse courteously: "I declined election to the National Institute of Arts and Letters . . . and now I must decline the Pulitzer Prize" (Sinclair Lewis).
Reject suggests the discarding of someone or something as defective or useless; it implies categoric refusal: "He again offered himself for enlistment and was again rejected" (Arthur S.M. Hutchinson).
If I have to put the difference in my words I would say:
Refusal usually implies determination and may or may not result in the final action.
He was forced to join the group even after his refusal to do so.
Reject & Decline can be considered a result (after-action) of refusal.
Rejection is often blunt whereas decline implies polite act of refusal.
This difference can be explained much better using your last example.
If the girl was polite and understanding then she declined.
If she threw vodka on the guy's face then she rejected. (wink wink)