I'm not social and so I avoid parties but if I were looking for a job, I'd make myself go to as many Holiday parties and fundraisers as possible.
There, I'd introduce myself to the people most likely to help me, and be my most engaging self: asking about them, listening well, asking follow-ups and talking about myself just enough that it doesn't seem like I'm interrogating them. My rule of thumb: talk 25-40% of the conversation.
Before asking for a job lead, I'd try to find an opportunity to help the person, for example, volunteer to help them with something, introduce them to someone they might like to meet, or even just give them some information they'd like to know. For example, if they love Thai food, I'd tell them about my favorite Thai restaurant.
That said, I would mention that I was looking for work. I'd keep it brief and positive, for example, "I'm looking for my next job. This time, I'm going after what I really want." (insert target work.)
If appropriate, at the end of a conversation, I'd hand the person an understated business card. VistaPrint offers great cards and THIS special discount link to VistaPrint offers unbelievable prices.
A day or two later, I'd send a hand-written note card to people with whom I've had a good conversation.
Send Holiday cards. Non-religious, peace-and-good-will-types are safe. If you insert a Holiday letter, mention your job-seeking only briefly and positively, per the above. Mail or email your cards early so people receive them in time to invite you to Holiday parties.
Volunteer. There are many opportunities during the Holiday season. It's a great way to meet other charitable folks as well as to make career connections.
The day after Thanksgiving and during the few days before Christmas right up to Christmas Eve afternoon, contact prospective employers. They're less likely to be busy and more likely to be in the Holiday spirit.