Can man use any of these words in daily life about anything in order to say "renounce", or there is some places that one does not fit?
closed as off-topic by Robert, user unknown, Hubert Schölnast, Stephie, LangLangC Feb 11 '18 at 14:19
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Short answer: no. They are not synonyms.
Entsagen and abschwören are very similar, though I would say abschwören is stronger. Both are a tad strong for daily life.
Abtreten (in the sense of renouncing) can only be used for something like an inheritance. And in contrast to the other two it needs a dative
Ich trat ihm mein Erbe ab.
From your previous question I think aufgeben is the best fit.