"it seems like a lot of the questions will never be relevant to me since they are extremely specific."
The first thing you want to do is select your "favorite tags" and "ignored tags" (see also: Expressing your tag preferences). The main effects of this are:
- In all lists, questions with tags you prefer are highlighted so they are more prominent while questions you wish to ignore are faded out and easily dismissed
- More importantly, it influences the algorithm that choses which question to display on the main page (see: Stackoverflow homepage changes).
With these in place, you are more likely to be presented with questions that you find relevant.
Naturally, it will take a while to come up a suitable list of tags. Start with a small set of "favorite tags" -- say math and java -- and gradually build on that.
"Is there some kind of advanced search which offers question with more than 14 votes && 7 answers && accepted?"
There is. See Advanced Super Ninja Search Options.
For example, here's a list of java questions with a minimum of 10 votes, 3 answers and 250 views, sorted by the number of votes. You can use the tabs just above the results to choose the sort order:

"I love SO and I am basically looking for gems since it is now the holiday season in Israel which means more time to waste"
If you're looking for gems to learn from, what I do is, when I find an answer that is enlightening and well written, I'll click through to the profile of the author and browse the list of past answers. Follow the trail of gems and you may just find a treasure trove.
The same goes for well written questions -- well thought out questions often lead to insightful answers.