Are all/most organic compounds non polar?

Question

Not all, certainly. Many are non-polar. Most, I don't know. It all depends upon how you define most. Acids, acid chlorides, amines, phenols, ketones, aldehydes, and the like are polar. There are a bunch of those around.

There are also compounds like sulfonic acids which are polar. Another couple of useful lab solvents that are polar are dimethyl sulfoxide (DMSO) and dimethylformamide (DMF).