The warthog is quite stable - so much so that unless you're missing control surfaces, it's pretty hard to get it to lose control.
Did you go through the correct startup procedure and enable the pitch & yaw SAS channels (pg 148 or so)? Also this usually isn't a problem (in the Sim) but did you make sure to press the Take Off Trim button until it lit, before taking off?
If you're using multiple controllers, some axes might be badly mapped and you'll have to sort that out in the controls options. For example when I first connected my Warthog stick, it made some very odd assignments (like assigning pitch up/down to rudder left/right). This might also happen if you have, say, an xbox controller connected as well. In some cases, two different controllers might be fighting for the same control axis which could only cause bad things.
If you press RightCtrl+Enter, a little overlay pops up of what it thinks your controls are set to, and where your trim settings are at. Try moving one control axis at a time and make sure it matches what you see on the graphic.
In terms of in-flight trim control, you should be using taps of the trim hat switch on the stick (or whatever you've got it mapped to). Normally you shouldn't need to mess with the trim knobs on the left panel, and you shouldn't mess with any sort of trim wheels on your joystick.