[susan53]

You were right when you said that had better is strong advice. The problem here is that in this situation "strong advice" is not appropriate - you are almost ordering your friend to come to dinner. had better is very close in force to should - it means the speaker is making a recommendation based on his/her own opinion, and will disapprove if the listener decides not to do it. For instance :
A : I'm getting really bad pains in my chest.
B : Oh no - that could be serious - you'd better go straight to hospital.
A: No, I hate doctors. I'll wait and see if they go away.
B : That's stupid!
In this case you have no right to "order" your friend to come to dinner, you need to invite him :
Would you like to come to dinner?
Do you want to come to dinner?
which allows him a free choice depending on what he personally wants to do. At most you could phrase it as a suggestion - "weak advice" :
Why don't you come to dinner?
How/What about coming to dinner?
Let's have dinner together.
Here the implication is that you think it's a good idea, but as it's only "weak" advice you won't be offended if he says no.