I'm now three years out of college, still trying to get a tech job (during the middle year, I was otherwise employed and not trying). My degree is a double major in CS / math

My deepest sympathies about your job search. The "double major in computer science and mathematics" part of what you wrote sounds scary, as I have a large circle of acquaintance among young people who are pursuing similar studies. I don't have comprehensive information about how the general mass of such students is doing, but I'll relate a few anecdotes that may suggest some paths forward for you.

Anecdote 1, a scary anecdote: A few years ago, that is BEFORE the financial system crash threw the world into recession, I had occasion to meet a young man who had been on his state's all-state mathematics team to compete in the ARML contest

http://www.arml.com/

during high school. Rather than stay in-state for his computer science degree, he went to another state to attend its state university (presumably on financial grounds). The other state's state university is a Big Ten university that ought to have a decent reputation for its computer science department. But as I met this young man, he was four or five months out of college, and living in his parent's basement while still looking for work.

Anecdote 2, a lot less scary: Another young person I know, nineteen years old (barely) just now, accelerated his high school studies by doing two years of dual enrollment (college studies as part of his high school program) with a grade skip or two thrown in besides. He did not participate in any formal mathematics competition programs. He then transfered to our state university as an advanced standing undergraduate, and finished up an undergraduate degree in computer science (with a few but not a lot of elective courses in mathematics beyond the computer science major requirements) before he was eighteen years old. Since he turned eighteen, he has been out on the west coast, and is now in Silicon Valley, telling many of his friends that there are a LOT of jobs for anyone who is a decent programmer. He programs for fun and has apparently always done well in his school programming assignments and in technical interviews. He is convinced that anyone who can get through a technical interview with coding work-sample testing can find a good job in Silicon Valley.

Anecdotes 3-5: I know several other young people who got various summer internships during various phases of their recent undergraduate studies in computer science at various universities, and once they made a good impression on one company by their work in the internship, they started looking around at other possibilities around the country. All of the better job opportunities seem to use the research-based process of work sample tests as part of hiring. One young person I know who is in the job search phase just now while wrapping up a summer internship has had full-day technical interviews with multiple work-sample tests and discussion of each phase of the work samples after each test. It's gratifying to hear that some of the young people I know are getting to the second interview phase at multiple companies and some others have started career jobs at Google (if that's the kind of job they like) or at brand-new startups (if that is what they like).

The crucial thing seems to be being able to do on the spot what industry jobs expect programmers to do. In the extreme case, people who can do that who haven't finished their college degree programs seem to be able to find career jobs. It doesn't sound like the degree as such is really the crucial hiring criterion in most places.

Is it, in your opinion, possible to have decent software development skills without years of experience under your belt? Do you meet many such people?

It is possible to have strong development skills without years of full-time employment in career industry jobs if one does the right kind of recreational reading and takes on challenging programming tasks "for fun." I know a few such people. For them, where they went to college, what they majored in during college, and whether or not they finished college seem to be almost incidental details about their biographies.

Good luck in your job search!