Every wedding I've ever been to, if it's a buffet-style dinner, has at least two meat choices and salad, and sometimes even mixed veggies. It's pretty easy to stay paleo at a wedding if you skip the rolls (which are always like bricks) and cake (which never tastes all that good anyway). Granted, you can never know how the foods were cooked, but I don't think it's worth the hassle to make the food an issue if you don't have a very serious allergy and especially if you aren't very close with the couple (i.e. going as someone's date).
As far as a birthday party, I suppose it depends on the menu. Are they serving a full dinner? if so, stick with a meat dish and maybe salad or veggies. If it's just appetizers, steer clear of the fried stuff and try to stick with the relish tray, meatballs, chicken wings (if they aren't breaded) and things like that. You probably won't know what the sauces and condiments are, and they probably aren't paleo, but you can stay pretty close to your goal.
If it is appetizers, offer to bring something paleo and awesome like bacon-wrapped asparagus. Or, just eat before you go. Nobody will notice if you aren't eating finger foods but they will notice if you skip an entire dinner when everyone is seated around tables together. If it's a home-cooked dinner and you actively choose not to eat anything, you will offend your host. You have to decide if it's worth it.