But because it's a small office, they must realize that the newest person hasn't been invited to the party, or been informed of the format and rules.
Not necessarily. In situations like this it's common for everyone to assume that someone else has taken care of things and not think much about it.
It feels more like they know I won't be here for long so there's no point in getting to know me or making sure I'm included in anything.
That may well be true but it doesn't mean they're deliberately excluding you from the party. The fact it's taking place in the office likely means they're assuming everyone in the office is automatically invited. I think it's still a good idea to check if you're expected to attend, bring food, a gift, etc. You can phrase it like "am I expected to..." or similar rather than "why aren't I invited?" because it'll come across more straight forward and formal, and if they have simply forgotten about you but didn't mean to, it gives them a chance to rectify it. It's not like they can say they don't want you there, seeing as you're working in the same office. If they really are expecting you to carry on working through their party, at least you'll know for sure in advance and can set up the Santa thing suggested above.
I have a sense of whose responsibility this is, and I don't think she really likes me enough to give a rat's ass.
If they really are being like that just be glad you're getting out of there soon. People like that aren't worth your mental energy and just wait for karma (if you believe in it) or the inner misery that drives them to be so spiteful to catch up with them.
I don't know the situation not being there, but I can see two distinct possibilities of what might be going on: 1. they really are being that nasty 2. it's all a big misunderstanding. In my experience, most conflicts within small groups of people come from misunderstandings and total failure to communicate. Granted that sometimes it's caused by one person who's a manipulative bully, but even in those situations, misunderstandings and failure to communicate make things worse.
If you've read the situation wrong, it will get extremely awkward. If you can clarify which it is with a simple question, you'll be able to do the right thing, i.e. join in with the party as expected OR set up the Santa thing. You'd avoid the whole thing of everything getting way more awkward due to a massive communication fail.
