I'd argue that there aren't really 4 "Presidents" in the executive sense, and that the lack of clear hierarchy between them doesn't mean that there's not a relative importance.
President of the Parliament
Notwithstanding that "In protocol ... terms, it is the President of the Parliament who comes first", that position is more akin to what would (usually) be called a Speaker in English -- it's not an Executive position.
Presidency of the Council of the European Union
The Presidency of the Council of Ministers (Council of the EU) is held by a given country at any one time, and is once again not so much an Executive Presidency as which country's Ministers chair the various committees.
President of the European Council & President of the European Commission
Arguably, one can't go far wrong if one thinks of the President of the European Council being nominally more important and setting broad strategy, while the President of the Commission is, day-to-day, practically more important and is responsible for actually getting things done. They could (with a bit of wiggling) be thought of as analogous to Head of State and Head of Government, i.e. the President of the European Council is akin to a President; the President of the European Commission is akin to a Prime Minister. There's a degree of split function between them, but that's also true of many countries (e.g. France, or Czechia).
From 1999–2009, there was a High Representative of the Common Foreign and Security Policy; since 2009 that has (following some changes to the position as well as the name) become the High Representative of the Union for Foreign Affairs and Security Policy (a.k.a. the EU Foreign Minister). Wikipedia claims (albeit currently without citation) that "The Clinton administration claimed in May 2000 that [the post] was the fulfilment of Henry Kissinger's famous desire to have a phone number to talk to Europe."
Who You Gonna Call
Sometimes President of the Council, sometimes President of the Commission, sometimes High Representative. But is that really any different from when a state wants to contact, say, the French Government?