Sounds like so much fun. When my mom turned 50, we had a 50's themed party and it was a huge hit.
I did a google search on 1960's era food, and found I had better luck ideas for menu ideas when I google'd 'Mad Men' party ideas. But from the ideas I got, here are some food.com recipes to try. Some I took some basic ideas and tried to find something a little bit more gourmet/fancy.
Dressed up Pigs in a Blanket #308183
Salmon Dill Deviled Eggs Appetizer #106988 (plus, there is one on Martha Stewart's website, that I have tried and were a hit with my family & friends)
Individual Beef Wellington #115129 or
Beef Wellington (((Wonderful))) #87185
Fruit Salad - Ambrosia Style #262042
Iceberg Wedge Blue Cheese Bacon & Tomato Salad #115216 or
Paula Deen's Wedge Salad #163596
Peanut Chocolate Parfait Dessert #134666
Plus, I would recommend having a bar with some popular 1960's era drink menus printed up on some fancy cardstock and having the appropriate liquors so the guests could make their own drinks. For some ideas:
Side Car #8442
Mint Julep - the Real Thing #128779
Canadian Whiskey Sour #310564
Tom Collins #192431
Bloody Mary #6449
Dry Martini #308774
Since you were wanting to add some humor, I though you could serve Tang and have astronaut ice cream available. I've seen the astronaut ice cream in novelty shops, such as Fuego or amazon.com.
Hope this helps. Have fun, can't wait to hear how it went.
KimmieCat