I know that Observant Jews are commanded by law to eat Kashrut or kosher, so can I as a Gentile invite my Jewish friend for dinner, for example at a marriage or engagement party? What food items should I offer him to eat? I know most of the things on our table may not be considered kosher as per halachik law, so my question is which food items I can offer him for eating, or is it better just not to invite at all?
You are certainly welcome to invite him. He can chose whether or not to come. If the food is being prepared in a non-kosher facility, really the only things that he would be able to eat without special effort are unprepared foods like raw fruits and vegetables. There are ways to make kosher food in unkosher ovens; however, that could take considerable extra effort (double wrapping everything, securing kosher food, etc.). I would recommend speaking with him personally to determine what his needs are.
There are many degrees and styles of kashrut observance.
Some people will be fine just by not mixing meat and dairy and excluding non-kosher animals. Others will politely refuse to eat anywhere that is not 100% kosher (which again, is a definition that might vary even among the most orthodox)
The best way to be sure is to ask your friend what his needs are. He will surely appreciate it.