The EU is not a democratic entity by any stretch of the imagination, it is anti-democratic, over-ruling elected members and overriding the wishes of the people.
Don't get me wrong: I would prefer for the EU commission to be elected more directly by the European citizens. And I certainly wish that the European parliament had more power. But keep in mind that the only reason it's not happening is because the various EU governments don't want to give up too much power: they have full control of the EU commission, but not of the EU parliament / EU citizens...
TL;DR: power in the EU is held by the European Council, that is to say by the head of states.
EDIT: typo
And how exactly are we going to hold the head of states accountable, so one could say we control him/her?
(Brexit - the movie). Sure, it's supporting Leave but the factual evidence is, well, just fact.
In your example you've said the EU "wants to" impose immigration quotas and "fine the countries that don't accept". How is that different from e.g. Germany imposing an immigration quota on your country? In exchange of e.g. not leaving you out of a trade agreement.
What's stopping your politicians from negotiating those quotas? Nothing, because that's what they're actually doing, but they know part of their voters are xenophobic, so they have to save face by saying "the EU told me to do it". It's politics 101.
Finally, please point me to where the EU is not a democratic entity, because I think I've missed the memo.