Can you play sacrificial offerings to wound your opponents character if you dont have a character for your opponent to target? If not then how does it stop the infinte combo of the large man and an offer you cant refuse?

Yes, you can play Sacrificial Offerings even if you don't have a character in play. In fact, that's probably the best time to use it!

The card's first effect is independent of the second. However, in order to enact the second half, the conditions of the first effect must be fulfilled. See page 6 (part 2.13) of the FAQ for a full explanation on how to use cards with multiple effects and the word "then".