Yosetsukenai = Repel?

Repel is definitely a better word. Expel means to eject or drive out. It's very frequently used to mean being permanently banned from one's school. It can also mean to be ejected, such as in the sentence, "a rock was expelled from beneath the lawn mower."

「英語で話すと日本のエンジニアは離れるよね。」　could be translated it in a variety of ways. Here's some examples:

「When (I) speak English, Japanese engineer's walk away.」

「When (people) speak English, Japanese engineer's walk away.」

These ones are more literal, as と after the root form of a word is usually translated as when. I'm not quite sure if this captures the meaning of the sentence properly though, so I'll write some sentences more true to what you said originally.

「Speaking English drives Japanese engineers away.」

「Speaking English repels Japanese engineers.」

What's the context of the sentence, anyway? Do you mean when you specifically speak English, or just speaking English in general?

Yes, you're right. If talks "expelled" Japanese engineers it would seem that there was some rule that banished all the engineers and prevented them from returning. If I "repel" someone, by some (usually gross) action I compel them to leave on their own accord.