Dear @SusieandBano,
congrats on the wedding plans and thank you for sharing your situation with us in the community.
As for your question, this question was asked in a similar way already, please follow the link:
https://***.wefugees.de/800495/can-a-refugee-get-married-in-greece-with-an-eu-citizen
Once you got married, you will have to apply for spuse visa in America and at the embassy in Greece.
I hope this could give you a first guidance.
If you have further questions please do not hesitate to address them here.
Best regards,
Nilab