Every handyman job is within every normal dude's repertoire provided they have the right tools for the job. It's just like opening a cork -- if you use a good corkscrew (or better yet, a power corkscrew), it's easy; if you don't, you're likely to botch it. When it comes to removing jammed, damaged or tamper-proof screws, you can either use your regular toolset or simplify your life by getting the Vampliers.
No, it's not a pair of pliers that look like Dracula. Or Edward. Or any of the dozens of nightcrawlers that Buffy slayed over many years. Actually, we have no idea why it's named like that, but I have to admit --
Vampliers sounds immensely better than super pliers or screw plucker or anything I can come up with.
The Vampliers can perform all the usual pincing and wire-cutting job of ordinary pliers, so you can use it as an everyday tool if needed. However, its true purpose is those specialized jobs of extracting erstwhile impossible to remove screws, whether they're jammed, rusted, damaged, stripped, or otherwise designed to be tough to pry off. It manages that by incorporating a patented jaw design that uses a mix of horizontal and vertical serrations that allow it to bite tightly onto any type of screw head, no matter how unusual or damaged it is.
According to the product page, it grips even better than locking pliers and screw extractors, allowing you to remove hard-to-pry screws with a lot less effort. The pliers are constructed from carbon steel, with the ergonomic handle grips made from rubber.
Amazon has the Vampliers available, priced at $35.