The USPS owns copyrights in most of its recent stamps, but U.S. stamps from before 1977 are not copyrighted. I don't know whether other countries claim copyright in their stamps. Even if they do, I think your collages would be permissible under the Fair Use doctrine:
* Your pictures are new and unrelated to the stamps (unless you're making collages that look like other postage stamps?)
* The source materials are ubiquitous, have already been bought and used, and have little residual value (except, occasionally, as collectors' items). In any case, the residual value does not inure to the benefit of the stamps' issuers.
* You are only taking unidentifiable pieces, and
* Your pictures have no effect on the market for new, uncanceled stamps.
I doubt you will have any copyright-related problems from your activity.
I agree with David's assessment that this is likely fair use rather than copyright infringement (at least under US copyright law). I would add that one practical consideration is that you do not want to have to face a claim for copyright infringement, even if you are on the right side of the fair use question, so some steps you can take to minimize any risk might be to use the smallest pieces possible (minimizing recognizability of any particular stamp) and use older stamps (as you've indicated you do). If you are planning to sell your artwork in a particular country outside the US, it would be a good idea to consult an IP lawyer in that country to ensure that no peculiar local laws apply.