Stranded cables are typically used in either fire alarm or audio
applications. Although you will find that alot of data patch cords too
are stranded.

Stranded cable is somewhat difficult to punch down both on jacks or
blocks but as long as all of your parts are rated at Cat 6 your service
should not be affected. Either a 110 or 66 block will work, I would
just take a moment to twist the pairs in one direction so they all are
punched in the same post.

Cross talk and next failures will result if you have stray wires
touching other posts either on the jack side or block side.

Another option on the block side, although a little bit more expensive
would be to install Cat 6, RJ45 mod ends on each cable. Your 66 block
and/or 110 block would need to be ordered with RJ45 jack type positions
built into either the side of the 66 block or under the first row on
the 110 block.

Whether you opt to twist your strands or install mod ends, you will
want to pair test your connection. If you get a good reading, the odds
are that you will probably never have to touch the termination again.
Changes to service would/could or should be made with your cross
connects.

Whether your cables are used for phone, DSL or extending your network,
I don't think I would go the extra expense to change now that walls are
closed up. I wouldn't use wirenuts either because the more terminations
a cable has the more chances for error.