visas – Entering the US with advance parole when having job and residence abroad or using ESTA

This weekend I have a flight to the US to attend a wedding. I would like to know what is the best way to enter the US without getting stuck at the airport or getting troubles to reenter the US in the future.

I am on advance parole, meaning that I waiting for an adjustment of status and the green card. I took a job in Norway and moved there two months ago. My intentions are to work and live in Norway, not in the US. I do not have a job or an address in the US anymore. For this reason I do not care so much about getting a green card anymore, so I would not mind too much is my green card application gets denied.

My questions are:

1) When I arrive at immigration, should I try to use my advance parole? If the officer asks about my address in the US (which I do not have anymore) I will have to say that I am living in Norway?

2) Should I forget about the advance parole and enter with a ESTA? Other than possibly losing the green card (which is not a huge problem for me), could I get in trouble (getting stuck at the airport, possibly getting denied to access the US in the future)?

Update: see my answer below