I think Ferro may have simplified things a little too much (and, maybe, got the emphasis the wrong way around).
Eurocontrol member states have signed up to a convention that says they will follow rules developed by the organisation. Thus Greece, being a Eurocontrol member state should implement the ESARRs - how this is done will be determined by the State in question but will almost certainly require legislation to be introduced. The SES regulations - which incorporate many of the provisions from the ESARRs - are directly applicable in all EU member states, that is to say, they exist within the legal framework of the State and will take precedence over any national legislation relating to the same issue.
The main weakness of the ESARRs was that although binding by international convention, few States took them very seriously and there were few if any penalties for not complying. The SES regulations are rather different and have a clear legal status backed by political will. As a result, few EU member states are particularly worried about the ESARRs now but are complying with the SES regulations. The outcome is much the same - because the rules are much the same - but there is a subtle difference!
To expand a little on your original question ICAO, like Eurocontrol, is based on an international convention. Again, States that sign up to the Chicago Convention agree to implement the Standards and, as far as is practicable, the Recommended Practices in their territory. The Convention makes provision for a State to file a difference if it is not practical to comply with a SARP (but, in theory, only for as long as it takes to achieve compliance). Again, like Eurocontrol rules, the State must somehow make sure that the SARPs are complied with - this usually takes the form of transposition into local legislation (although there are other ways of achieving this, in the UK for example, much of the ATM related Annexes is not transposed into legislation but rather into regulatory requirements). The status of PANS is not the same as standards and there are differing views on the topic but a reasonable line to take seems to be that they are the equivalent of Recommended Practices - as the introductory text to Doc 4444 says 'the PANS are approved by the Council and recommended to Contracting States for worldwide application'.
As to TCAS-RA and ATC order conflict (I'm not quite sure what you mean by the latter) you won't find anything that specific in either the ESARRs or SES regulations, both sets of regulations are high-level and objective based. The SES regulations make provision for the development of further Implementing Rules (although not predominately for operating procedures) so it is possible that more detailed regulations might appear in the future.
All that said, you need a crystal ball to even guess at how things will change if, or as seems more and more likely, when EASA take over responsibility for ATM. The early indications are that they want to see a different regulatory model applied with far more detailed regulations legally enforced.