I can't find the steward In Morthal and the Jarl won't send me on quests.
I have Hearthfire and a house in Whiterun and Falkreath. I am thane in both.
Do I have to be thane in Morthal as well?
Try talking to the Steward during business hours (8AM-8PM). He should be in the halls or somewhere in Morthal. Yes, you must be a Thane in Morthal in order to purchase a house.
If this does not help, here is a link that describes something similar to your problem.