Irish87

No expert on this, but think you should realize once you go down that road, you cant leave the USA until AOS is over. they may not let you back in if you do

Sounds like you should be just fine, just be sure to follow the guides to the letter. My husband is from Ireland and just finished adjusting after a 2 year overstay, no problems

If AOS is denied(aos from tourist visa), then you can't use VWP again and you can't appeal the decision because you sign away that right when entering on VWP. You'll have an overstay from the time your lawful stay is up until leaving, most likely resulting in a ban and in which case you'll need a waiver when filing a new petition and having the interview in home country.
It's good to know what your alternatives are however a few things to point out;
You don't have to prove that you didn't enter with the intent of immigrating. They already determined that by letting you enter. What is the dealbreaker is if you lied to a CBP officer and they took notes of it. At any point of time, you may be questioned about that, and if on file, USCIS has access to it. That means saying you're visiting your aunt when you've had a relationship with your wife/gf for 3 years is misrepresenting yourself. But again, by being let into the US, they already believed that you didn't have immigrant intent.
But nothing is stopping you and you can try to submit AOS after marriage. Just remember to please please please read the guides and especially the instructions for i-130 and i-485. When having an interview in the US(AOS interview), the overstay is automatically forgiven as you are the spouse of a USC.

Read the guide up top for spouse inside the US. You did not have intent to immigrate when you came, so you can go ahead with the Adjustment of status. Note you will also need an affidavit from your future wife, even if it says zero income. The Father in law is the co-sponsor. Good luck.
Edit for above: Once the AOS is submitted for initial review, the immigrant begins a NEW period of authorized stay. If it was denied for some reason, the pending time would not turn into overstay. In other words, no ban would be incurred.
OP: It is true that there is no appeal from AOS from VWP, but if you relationship is real, and you are not otherwise inadmissible (have a criminal record) then there is little to worry about.

Have fun getting married!

You can marry and file for adjustment of status. The most likely result is approval but there is no gaurantee at all.
In total it's around $1500+ medical and you will still need to meet the income requirements.
There is no gaurantee you will be approved and I believe there is no appealing from a vwp adjustment (could be wrong here).
Edit: if you are denied you can return to Ireland and file CR-1 and that's fine.

Yes the affidavit is what you need, he needs to show he can support the whole family 125% of the poverty guidelines.
If your AOS is denied it wont affect your CR-1 application apart from you wasting nearly $2,000.