お陰(かげ)でThanks to, Because of

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.')

ために and せいで can both express the idea of 'due to (A)', but they differ in that おかげで almost always describes a desirable result, while ために can be used with either a positive or negative nuance. ために can also, in some cases, mean 'for the purpose of (A)', while おかげで cannot be used in this way.

Both express cause and effect, but with different tone and usage. おかげで implies a positive result and gratitude, e.g. 先生のおかげで合格できた ('Thanks to my teacher, I passed.') そのため(に) is neutral, objective, and often appears at the start of a sentence. It can also mean 'for that purpose'.

Both express cause, but differ in tone and formality. おかげで implies a positive result with gratitude, e.g. 先生のおかげで合格できました ('Thanks to my teacher, I passed.') につき states a neutral reason, often used in formal notices, e.g. 雨天につき中止します ('Due to rain, it is canceled.') It also only follows nouns.