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You gotta be careful with that one so you don't offend anyone. "Yourname and Fiancename were married on Date. You are invited to a celebration reception"

Then list the date/time/place. You can include reply cards or an insert telling them to go to rsvpify.com to reply to make sure you get accurate numbers for your venue/vendors.

I think your parents need to make it very clear to them that this is just an engagement party, however you will be a ‘eloping’ so to speak. Wow that’s a tricky one. I personally would not get offended at all, but I know that there are people out there that might get offended by it, which is ridiculous to be honest, but who cares about those people. Just tell your parents to make sure that they let everyone know that they are hosting the engagement party and it is completely separate from your wedding

I didn't catch from your wording if the party is before or after your elopement. If it's before, then you really shouldn't invite anyone to the party who isn't invited to the elopement. However you can invite people to a post wedding celebration afterward.

Well, I would think it would be a reception without the wedding ceremony like a lot of brides are doing now due to Covid. I was recently invited to a wedding reception and told the ceremony was a family event, due to location. I wasn't offended. I think a lot of people would rather be at the party/reception over the ceremony. You could just say something like: Due to logistics, we will be having a small intimate wedding ceremony but would love for you to join us at the party/reception...

Personally, I would advise that this party take place after the wedding. While there will still be some uppity guests who take offence at not being invited to the wedding, by having this party after the wedding, you avoid any possible instances of giving any guests the wrong impression as to whether they are invited to the wedding. I.e. party pre wedding gives off 'engagement party' vibes, while a party post wedding will be more 'celebrate our union' if you get what I mean?

Agreed that this party should take place after the ceremony has already happened. I'd send out "marriage announcement" cards that includes wording about a "celebration of marriage."

Start at the top saying that Sue and B obwill be married at a small private wedding on ___date__.
The rest, standard invitation to a formal/ informal reception in their honor. These have always gone o, not just due to covid.