stickery? as in small spines along/around the length of the
stem, which is prostrate?
those aren't strawberries. they are likely what we call
'dewberries', a prostrate & not very fruitful form of
blackberry.

Ah, yes, seems likely: http://en.wikipedia.org/wiki/Dewberry

My first guess was some kind of raspberry/blackberry, but I didn't
know that there are some which stay close to the ground. We have some
weedy raspberries (or such such) in our yard, which don't seem to
produce any fruit, but they are somewhat more upright.