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Generally 抜く means to pull out something long and narrow from a hole or similar place. Usually the thing you pull is sticking, clogging, closing, occupying or jamming. It is one of the most frequent words and has various usages; it's like asking what "get" means. These are some typical examples:
白髪を抜く pull out a white hair.
ワインの栓を抜く open a bottle of wine. (栓 is a stopper, so in this case it means a cork.)
刀を抜く draw my sword.
DVDをドライブから抜く take the DVD out of the drive.
本を本棚から抜く choose a book from the bookshelves.
風呂の湯を抜く let the water out of the bathtub (A water outlet is a hole and water through it is considered kind of narrow).
財布を抜く pick a wallet ("Pick" in this example is kind of "steal" + "pull out," so you use 抜く).
Some words collocate with 抜く. In such a case, the sense of "remove" or "take out" is often emphasized:
インクの染みを抜く remove an ink stain.
脂を抜く remove the fat.
髪の色を抜く bleach the hair (you're "getting rid" of a pigment.).
力を抜く relax (in the sense of "try not to be nervous" i.e., "get rid" of tension).
昼食を抜く skip lunch.
Another important meaning is to overtake/pass:
先頭走者を抜く overtake the lead runner.
There are millions more usages, but I think you can get the gist of any sentence if you grasp the basic meaning unless it's an idiom. Most of the time 抜く means either "pull out," "pick out," "get rid of," "omit," "scoop," "takeover," "pierce" or whatnot.
The other words you asked are also very common so it's hard to give concise definitions and make you understand by few examples. If this post helped a bit, I might post definitions and examples for other words when I find time.
Maybe it'll be helpful to ask a native Japanese speaker who speaks English better than I do to translate the pages for the words in a monolingual dictionary for native Japanese speakers.