I have read the related questions on "how to politely reject a wedding invitation", but my case is different.
In my Sri Lankan culture/tradition, the invitation is given by personally visiting the cubicle, not by email. In this case, how to politely decline it?
One suggestion I have been given is to give them a card with a note thanking them for the invitation, along with a little gift and an apology stating that I cannot attend due to other commitments.
There are a number of cultural issues that I am trying to avoid in the workplace:
Not accepting the invitation means disrespect. It is like saying, "Hey, I don't care what you said" or "I don't have time to care". This may affect promotions and salary increments too.
Accepting the invitation and not going to the party, also shows off disrespect to the money and the effort he/she spent for you. This seems rude.
Not giving a gift. This does not show any disrespect, but indirectly shows that you are financially weak and not suited to attend parties of their social status.