Advice for Removing Raceway Wiremolds
You could try running a putty knife or something behind them, but my actual advice for removing them is to have the spackle or drywall compound and paint handy, as scars are to be expected.

Hmm - heat  (as from a hair dryer - not so much as to scorch paint) might also help loosen the adhesive a bit.

As for the left-behind adhesive the usual suspects - goof-off, paint thinner, cleaning sprays, try various things looking for one that gets the adhesive but not the paint, or wait for a more specific suggestion here from someone who's done it recently.