How should I cut odd angle miters when working with molding?
The standard way to cut mitered corners is with a miter saw, either a hand saw with a miter box or a power miter saw.

I don't know how you're cutting your 45ºs currently. If you're using a hand saw and want good control, I would get a hand miter box with an adjustable angle, like this one on amazon. Usually they have stops at common angles like 45º and 22.5º, but you can set it to any angle (I don't have any experience with this model though): 

If you want something quick and dirty I would just use a carpentry protractor / angle finder to draw a line and then freehand it: