on Sundays and every Sunday

They are not interchangeable.

"He goes to church on Sundays" would imply frequent Sunday church attendance, but "He goes to church every Sunday" would mean (almost) invariable Sunday church attendance.

"He goes to church on Sundays" might also mean that Sundays is the day he goes to church, as opposed to Saturday, without implying anything about the frequency of attendance.

"He does not go to church on Sundays" means that he almost never goes to church on any Sunday, while "He does not go to church every Sunday" means that there are some Sundays he doesn't go to church.

The short answer is that they are not interchangeable.

On Sundays

This provides a condition to when the event happens, but doesn't necessarily speak to how often it happens.

For example, imagine a church which provides service on both Sunday and Wednesday. Saying "He usually goes to church on Sundays." tells us that he usually attends the Sunday service, but not the Wednesday service.

However, it doesn't tell us that he goes to church often; only that when he goes, he goes on Sunday.

Every Sunday

This provides a condition on how often an event happens, but not necessarily additional restrictions about when the event happens.

For example, in our previous example, saying "He usually goes to church every Sunday." tells us nothing about whether or not he attends church on Wednesday. Whether or not he attends church on Wednesday, it wouldn't change the sentence, as long as he attends church most Sundays.

In some contexts, they are pretty much interchangeable, but "on Sundays" could mean some Sundays, while "every Sunday" means all Sundays. In your example, "He usually goes to church on Sundays" means that Sunday is the day he goes to church (which would make going to church on another day unusual, while "He usually goes to church every Sunday" means that he always goes to church on Sunday, unless something stops him (which would make not going to church on a given Sunday unusual).

To give another example, "I go to the beach on weekends" means that I go the beach on some or all weekends. On the other hand, "I go to the beach every weekend" means that I go to the beach on all weekends.