せいでBecause of, Due to, Blame

Both せいで and につき express cause, but with different nuance and tone. せいで is more colloquial and typically introduces a cause for a negative result, e.g. 雨のせいで試合が中止になった ('The game was canceled because of the rain.'). につき states a reason more neutrally and is often used in formal written announcements, e.g. 工事中につき通行止め ('Closed to traffic due to construction.').

ために and せいで can both mean 'due to (A)', but with a difference in tone. せいで almost always implies a negative or undesirable result. ために can be used with either positive or negative nuance. Also, ために can mean 'for the purpose of (A)', which せいで cannot.

Both mean 'because of', but with opposite tone. おかげで expresses a thankful cause, e.g. 先生のおかげで合格できた ('Thanks to my teacher, I passed.') せいで places blame for something negative, e.g. 雨のせいで試合が中止になった ('The game was canceled because of the rain.')

Both せいで and そのため(に) show cause and effect, but せいで follows a word or phrase and implies a negative result or blame, e.g. 台風のせいで試合が中止になった ('The game was canceled because of the typhoon'), while そのため(に) is used at the beginning of the sentence and neutrally shows a logical result of whatever was previously stated. そのため(に) can also express 'for the purpose of (A)', which is a nuance せいで cannot have.