Here are some common expressions you can use when making or responding to invitations.

Inviting somebody to do something

We’re going to the movies tonight. I thought you’d be interested in coming.
I’ve bought two tickets for the concert. Would you be interested in coming with me?
Would you like to go to the theater tonight?
I was wondering if you’d like to eat out tonight.
How about going for a long drive?
How about going to the movies tonight?
Would you like to come over for lunch?
Would you like to eat out tonight? They’ve just opened a new Chinese restaurant in the town.
Would you like to come over for a drink?
Care to come over for dinner?
Care for a drink?
I’d be delighted to have you over for my birthday party.

Accepting an invitation

Here are some phrases you can use to accept an invitation.

Sure. What time?
Yes, I’d like to come.
Sure. When should I be there?
Sure. I’d like to.
Thanks for inviting me. I’d like to come.
That’s very kind of you. Thanks.

Declining invitations

Here are some expressions you can use to politely decline an invitation.

I’m sorry, but I can’t come. I’ve got too much work.
I’d like to come, but I’ve already made some other plans.
Tomorrow looks difficult. I’ve an appointment.

I’d like to come, but I can’t. I’m supposed to be doing something else tomorrow afternoon.