であれEven if, Even, No matter

Both can mean even if or no matter, but nuance differs. にせよ・にしろ stresses the speaker’s strong insistence, as in 学生にせよ社会人にせよ責任はある (Even if you’re a student or a worker, you have responsibility). であれ is more formal and written, as in 理由が何であれ許されない (No matter what the reason, it’s unforgivable).

にしろ～にしろ can follow verbs and broader phrases, as in 勉強するにしろ遊ぶにしろ全力でやれ (Whether you study or play, do it wholeheartedly). であれ follows nouns, な-adjectives, or wh-words and is more formal, as in どんな結果であれ受け入れるしかない (Whatever the result, we must accept it).

These are essentially the same grammar point, expressing no matter if one thing is true, the result does not change. The difference is that であれ～であれ is specifically used when comparing multiple options, e.g. 子どもであれ大人であれ 'no matter if they're a child or adult', while であれ is used with single examples, e.g. 大人であれ 'even if they're an adult' or with question expressions, e.g. 誰であれ 'no matter who it is'.

何しろ appears at the start of a sentence to give a reason, like after all, as in 何しろ忙しいので行けません (After all, I’m busy, so I can’t go). であれ follows nouns, な-adjectives, or wh-words to mean even if or no matter, often in formal contexts, as in 理由が何であれ許されない (No matter what the reason, it’s unforgivable).

とはいえ and であれ are similar in that they both express a sort of contrast, but とはいえ 'although (one could say)' specifically qualifies a statement by saying one thing might be true, but there is more to the matter, e.g. 日本人とはいえ、フランスで生まれ育った ('Though she may be Japanese, she was born and raised in France.'). Though they can overlap in some cases, であれ 'even'/'no matter' is often used together with question words, e.g. 理由は何であれ 'no matter the reason', while とはいえ cannot be used this way.