Depends on what you're looking for -- when you say "illustrations" I'm thinking something along the lines of the complexity of an average cartoon character. It's hard to find public domain illustrations like that, but you can get them for free -- just find some you like on DeviantArt or another open art forum, and contact the illustrator and ask for permission. Some will ignore you, some will say no, some will ask for a royalty, and some won't care as long as their name can appear on the finished product (which on a birthday invitation is certainly easy, since most have copyright info on the back.)
What I mean is, sources for that are generally abundant, but require some digging. Sources for available photography are much easier to find, since photographers usually are pretty specific in their licencing requirements.
You can check on Flickr using this search string:
Where "keyword" is obviously replaced with your keyword (for more than one word, use a plus sign to separate them. That search will show only photos that match your keyword, plus have been licenced under CC with explicit permission by the artist for the picture to be modified and resold without royalty. Unfortunately that only applies to photographs.
You could also just pay someone to create the images for you. I realise that you said "free," but line artists are cheaper than you might think; plus, a one-time expense for a given image can be paid for many times over in sales if the card ends up being popular.