する(しょうきょ) Eliminate (process of elimination) or delete (computer term).
する(さくじょする) Almost the same as 消去, but much more widely used。
(のぞく) The more hostile meaning is, to exclude, for instance:certain people. Or, more politely, to not count someone:“Not counting Bill, everyone here is republican.” “Not counting Sarah, everyone here hates cats.” “Except for one mistake, he did a good job!”
(とりのぞく) – almost the same as 除去:to remove, to clear away, get rid of (garbage, weeds, etc.)   $$$
(じょきょ) Eliminate or remove a physical thing:(bugs from your garden, harmful chemicals from the solution, a tumor from your lung) less used than 取り除く, but more official or formal-sounding.
(かいじょ) To rescind a set of rules, sanctions, etc. Quite official.Also has a legal meaning of terminating/cancelling something eg 契約を解除する: terminating a contract
(はぶく) To omit (usually used about omitting things when you speak).  Omit the formalities. To skip over. Use the tivo to skip the commercials. To do without. To omit certain time-consuming rituals from your wedding ceremony. In contrast to 消去、省く means to skip over (this time) rather than delete permanently.