Jo King,
Cross rhythm is sort of the same as syncopation. I define it as any rhythmic pattern where the accents are not always falling on the main beats of the measure.

Polyrhythm gets used in a couple of ways: the dictionary definition is two contrasting rhythms being played against each other. Lots of folk musicians use the term to describe time signatures that are not the "normal" ones like 3/4, 4/4, and 6/8. You can hear a lot of 5/8, 7/8, and 11/8 in Bulgarian music and elsewhere.

You might be able to get some more specific advice if you told us which sorts of music you are interested in learing the rhythmic patterns for.

I always advise people that are trying to learn rhythms to drum along with the type of music they want to learn. You can drum along by beating on your legs with you hands -- no investment and no learning curve. Learn to play the rhythms while you don't have your guitar in your hands -- do one thing at a time. If you can get your body to know the patterns, when you pick up the guitar, your body will still know the patterns and will take over your strumming hand.

John Peekstok