Incur, contract, catch are comparable when they mean to bring upon oneself something unpleasant, onerous, or injurious.
Incur may or may not imply foreknowledge of what is to happen, but it usually implies responsibility for the acts which bring about what is incurred.
Contract carries a stronger implication than incur of acquirement, but it is equally inexplicit in its lack of clear suggestion as to whether the acquisition derives from intention or accident. But contract often distinctively implies a meeting between two things that permits either an interchange of qualities or a transmission of something from one to the other.
Catch, the least literary and most ordinary of these terms, usually implies infection or something analogous to it.