Something isn't adding up. You just got back from a week-long vacation, and you received three voicemails from the firm (the last one being last Monday). Did they really call on consecutive days, or was a voicemail left before you left for the trip?
Either way, you need to call HR first thing the morning and explain that you were on vacation. You need to emphasize that you had provided them with your cell phone as your main form of contact, even if that wasn't the case (you have nothing to lose). However, you cannot turn it into a blame game. As soon as you start accusing the firm of screwing up, that's when it's game over.
If things don't work out with HR, you need to call your interviewer and anyone else you know at the firm. As long as you're nice about it, you should be fine (unless they already gave the offer to someone else).
But for future reference, never give out your home number. There's no reason to.