Some of them are pretty restricted (and I see 移動 is listed twice), and you can see how the meanings are derived. “Transfer” is a fairly basic concept after all.
乗り換え means to transfer from one mode of transportation to another, such as from one train line to another train line.
振替 expresses an idea of switching something from one thing to another. It’s also used for money transfers.
移動 is a general word for motion, so it can overlap with general concepts of transferring as motion in English, though to be honest, I don’t feel like we use “transfer” in English the way 移動 is used in Japanese. It would have to be a very specific situation.
転送 is used most often in the concept of forwarding an email.
移譲 is used to talk about transferring wealth or rights from one individual to another.
To me, the kanji tell the story, and fit well with how they are limited in use. Some of them come up less in everyday use, but there is no “generic” transfer word you could apply to these concepts.
I feel like Japanese people would not consider most of these synonyms at all.