A curse increases the death value of your character... how do you get rid of the curse?

 Curse Doll

Discard after equipping at the start of your turn to remove up to 3 effect tokens that have been placed on you.

Thatis it? An item? Theres no way to buy your way out of a curse at the temple or something?

Nope. Dying or a Curse doll are the only ways. 

Mind you the Curse Doll is pretty much "buying your way out of a curse" in the first place. It's 200 gold and it's in the Town Shop deck.

Do you remove curses and poisons after going back to world map?

Im only a beginner but I would answer no... just as your health isnt restored automatically, curses and poison arent either. Only fatigue restores automatically, and I guess there are a couple characters (Scorpion comes to mind) that have exceptions.

 Further question - does the OL gain threat for every curse, or just ones from treasure?  If Brother Glyr kills a Dark Priest, or if Tahlia equips a cursed Skull Shield, does the OL gain +4 threat?  

The designers have misleadingly used the word "curse" to describe two completely different and unrelated things:

Curses are found (only) inside treasure chests, and give the overlord 1 threat per hero (per curse).

Curse tokens are a status effect that increases the conquest value of a hero.  They are gained by equipping cursed items or dealing the killing blow to a monster with the Black Curse ability.  They do not interact with threat in any way.