Within linguistics, the terminology for parts of words varies according to theoretical perspective. Commonly, though, they are called morphemes.
Morphemes are frequently divided into various kinds, most basically, roots versus affixes. Roots are “open class” items, like objects (cat, chair, paper) or actions (run, arrive, fall), whereas affixes are “close class” items (such as the verbal endings ing, s, ed). That is to say, within a language, the stock of roots is large and expandable (when you encounter a new animal or invent a new gadget, you can coin a new root), whereas the set of affixes is small(er) and generally fixed (people rarely invent new verbal affixes).
Returning to your question, you can refer to para, sol, jay, and walk all as morphemes. Of these, para is an affix, and sol, jay, and walk are roots. Being a combination of two roots, jaywalk is said to be a compound (and, given that you can’t derive its meaning from the meanings of its constituent morphemes, it is said to be semantically opaque, or idiomatic). The root sol (also found in solar, solarium, solstice) does not occur in isolation (as a freestanding word sol), unlike jay and walk. So, it is called a bound root (or a cranberry morpheme, after the cran or cranberry, which also does not occur in isolation); jay and walk are free roots.