Ball hits elbow or below elbow of batsman and raises in the air. The ball is then directly caught by fielder. Is he out or not?
Almost certainly not out. Refer to Law 33.1 "Out Caught"
The striker is out Caught if a ball delivered by the bowler, not being a No ball, touches his/her bat without having previously been in contact with any fielder, and is subsequently held by a fielder as a fair catch
contact between the ball and any of 22.214.171.124 to 126.96.36.199
188.8.131.52 the bat itself
184.108.40.206 the batsman’s hand holding the bat
220.127.116.11 any part of a glove worn on the batsman’s hand holding the bat
18.104.22.168 any additional materials permitted under 5.4
shall be regarded as the ball striking or touching the bat or being struck by the bat.
"The elbow" is not listed in any of the points in 5.6.2 so the ball does not count as having struck the bat, so the batsman cannot be out caught. The batsman could potentially be out LBW if the ball would have struck the wicket - despite the name, this does not have to involve the leg.