My head coach's defensive style is a preference for a 3-4 formation. Yet when I let the coaches pick my defense they don't choose any 3-4 formations. So what exactly does the coaches style mean??

I believe the head coach sets the overall parameters like defensive and offensive style

There are two things that the coaching style influences:

1) The default player weights/recommended weights (under MyTeam->Edit Player Weight)
2) The plays that are in your playbook.

This only applies to the head coach, the other coaches' styles have no impact, they are just visible so that you can know what they are if you are wanting to hire one as your head coach.

I have a question relating to coaching style, does the team, players or relatively anything have an affect if say you have your head coach, off. Coordinator, defense coordinator, and some positions coaches all have the same offensive or defensive scheme?

That could be an interesting concept, might be a little tough to put the pieces altogether.

No, not right now.