How do you avoid offending??

Do they make a salad too? Eat a huge salad and a piece of fried whatever. There's usually a way to stay within your calorie goal.

Tell them the truth. And bring your own back up food just in case needed. I even now carry my food scale in my purse if I know I am going to eat at some ones home. This way I can weigh my food just as I would at home.
I may get a odd look at first, but I simply explain, " hay on a diet, I have been doing good, and don't want to get off corse with it so got to do my thing". They understand and tell me they are proud of me.
Of corse I have gotten the " oh you can take a night off tonight and just eat what ever." I simply say , nope. Sorry my nights off are rare. Maybe once a month and for holidays mostly. Plus I don't feel like spending the extra time at the gym tomorrow trying to burn off extra calories.

That's a hard one, but you'll just have to either eat it or tell them.

Sounds like a tricky situation. I've dug many an unintentional hole with members of my own family in similar circumstances. Start by telling the truth about choosing a healthy lifestyle and let them know that your diet is a big part of the changes you are making. Since the gathering is on the weekend, perhaps offer to bring a plate of food to share. This shows them that you're serious about the changes and gives them an opportunity to try healthy eating for themselves.
Perhaps the reason they don't understand 'healthy eating' or 'portion control' is because no one has explained it to them. (or maybe they just don't care)
If they don't like what you bring, then there's more for you.
If you don't want to eat the food they serve or large amounts of it eat something healthy before you go and you won't have real estate in your stomach for the fry up.
I've had many criticisms from family members about my eating habits "You don't need to lose 'that' much", "why don't you eat 'real food' any more", "Isn't my cooking good enough for you now", "surely you could have one [insert unhealthy food/drink here]". Honestly, it's a challenge to keep my cool sometimes but, I try to keep things positive and all about my choices rather than returning the criticisms. It works for me most of the time although, some people are easily offended (no matter what you say) so you might just have to accept that they'll take offence anyway.

Can you ask your partner? It's likely you'll get a better idea than any of us could give you, since we don't know these people.

"No, thank you" and "Yes, I'm sure, thanks" work okay most of the time.

In my experience people don't really notice what you eat. After a dinner party I would have no idea if one of my guests didn't eat mashed potatoes or bread or left half their dessert. I would take a little of what she cooks and maybe leave some on the plate, keeping under the radar as much as possible. Mush it around like when you were a kid so it's less obvious.