"Pretty" is being used here as in "pretty much" of something, or "that's a pretty big load", or "that's a pretty ugly dog" - indicating a substanial degree; nothing to do with the other meaning of pretty, i.e., "mildly beautiful".

"Dodgy" is not as commonly used in North America. It means "worthy of suspicion; possibly dishonest; on the borderline of illegality or immorality". From the idea of someone dodging around to avoid the authorities.

"this song is highly offensive"

That was my initial reaction, and I think it would be the reaction of most people. However, upon reflection, I find it (disturbingly) ambiguous (as I mentioned).