脑袋 vs 脑子 vs 头脑 vs 脑筋
脑袋 is literally referring to the head, the biological head of a person.
脑子 is also referring to the biological brain. You can say

他的脑子里有许多奇怪的想法 means he is having a lot of weird thoughts in his brain
他脑子不好使 means he is not smart

头脑 and 脑筋 are similar, they both mean mind in some way, but are used in different places

他很有头脑 means he is a smart guy
脑筋急转弯 is a puzzle game like the following
Who is closer to you, your mom or your dad?
Mom is closer, because dad is farther.

头脑 and 脑筋 are most commonly used in those two places, so you are good with them once you have those two examples in mind.