What are the differences between these verbs?

Question:

They all seem to mean the same or very similar things in there groups. Please define them and use an example sentence. If I put the wrong word (under the wrong group), please tell me what the correct word would be Thank you!

To Go Back?:
退く　（のく）
退ける　（しりぞける）
退く（しりぞく）
退く（どく）
退かす　
退ける（どける）
取り去る
持ち去る
連れ去る
戻る
引き返させる

To stop?:

止める　（とめる）
止まる
止める　（やめる）
つまずく

To remove?:
退ける（どける）
取り除く
解雇する

And how do you say to quit?

Answer:

You have to combine "go back" and "remove" group because some verbs have the same meaning.

退ける　（しりぞける）: This has many meanings like "dismiss (a lawsuit)" "reject" "withdraw", It depends on context which one is the most appropriate. And this is a transitive verb.
退く（しりぞく）: This is an intransitive verb of 退ける.

退ける（どける）: This is "remove", transitive verb. Or "moving something to another place."
退かす: Basically the same with 退ける　
退く　（のく）: These 2 are an intransitive verb of 退ける. Used when someone changes his place to let someone walk through.
退く（どく）

取り去る: These 2 mean "take something and run away"
持ち去る
連れ去る: This is used on someone who is "taking someone and run away". It sounds like kidnapping.

戻る: This is simply "go back" or "return"
引き返させる: This means "let someone go back or return"
取り除く: This is "remove"

解雇する: This is "dismiss employees". So it must not be in this group. This is very different from others.

To stop?:
止める　（とめる）: This is "stop" transitive verb.
止まる: This is an intransitive verb. You yourself stop.
止める　（やめる）: This is the same with とめる. But とめる is used when something with figure like train or car is stopped. やめる is used when you stop something without figure like job, study, etc.
つまずく: This means "fall down while walking". Or as its derivative meaning, "fail in something"

>And how do you say to quit?

It depends on context.