Cut the Jamb and Pull
You can knock a jamb sideways out of its opening, but the nails or screws holding it in place put up strong resistance to the shear force you apply.
An easier way is to cut one of the sides in half with a reciprocating saw and then pull the rest straight away from the framing. You can easily pull away any nails or screws holding the doorjambs in place simply by using the leverage of the jamb itself. Make your cut at an angle so the two cut sections don't wedge against each other, preventing you from pulling them apart. This same technique works for pulling out windows.
Pull Nails With a Nipper
If you're replacing windows, doors or flooring and you want to salvage the trim, end-nipper pliers are a handy tool to pull out brads and finish nails. The rounded end provides plenty of leverage, and if the nail breaks, you can always cut it down flush. Don't squeeze too hard when gripping the nail or you may nip it off prematurely.
Pull Drywall Screws
When you pull drywall from a wall, the screws usually stay in the studs. Unscrewing them with a drill is not the most efficient way to remove them because the screw heads are usually deteriorated or full of drywall mud. Use a pry bar or your hammer claw to pull them out just like you would with nails. Drywall screws are brittle, so if some joker used 3-in. screws to install the drywall, snap them off with your hammer.