Refers to one's spouse's father. The most common meaning.
義父は来月定年退職します。
My father-in-law will retire next month.
A man who raises a child as his own without being the biological father. Less common than father-in-law.
彼は幼い頃から義父に育てられた。
He was raised by his foster father from a young age.
A man who is married to one's biological mother but is not one's biological father.
義父とは最初はぎこちなかったが、今は仲が良い。
At first things were awkward with my stepfather, but now we get along well.
Next week I'm going to meet her father-in-law for the first time.
After getting married, we ended up living together with my father-in-law.
My wife works while also taking care of her father-in-law.