“Wouldn’t it have been weird if they (had) made you study engineering?”
The past conditional describes a situation in the past that never happened, or did happen and the speaker is describing the possibility of something not happening (or happening) in the past. This is also called the unreal conditional.
Here’s an example:
“If I had finished high school, I would have gotten a good job.”
(Situation: I didn’t finish high school; therefore, I didn’t get a good job.)
The “if” part of the sentence uses the past perfect: “If I had finished high school.”
The “would” part of the sentence uses the present perfect. This is the likely result: “I would have gotten a good job.”
You can invert the clauses:
“I would have gotten a good job if I had finished high school.”
In this case, no comma is needed.