I believe that Thank You notes are not required for a birthday party when the giver is thanked in person, especially if gifts were subtly discouraged beforehand.
It's cute, though, to send a scribbled card with a photo to family members.
For non-family guests, I'd skip the TY notes. It's not necessary, and if it becomes expected, it will be a burden on parents.
I'm not sure why this should be a problem. TY notes were never expected of me and I never knew to write them until I became an adult. In fact, no one at my bridal shower received a thank you note, much to my embarrassment. I'd rather be inconvenienced as LK grows up so that she learns the value and importance of a thank you note, rather than have her reach adulthood never having experienced the "burden" of them.
I'm willing to be burdened for a few years. It's not a big deal.
How many times have we read stories on the main blog where the writer has been offended that they "never got a thank you note, either." (Usually this is in addition to other bad behaviour.) Getting in the practice of writing thank you cards now sets a strong example as she gets older. I think learning to write a thank you note is an important part of learning good manners in general. Eventually the burden will be lifted off me as she goes from a little scribble to a big and messy "Thank you" to a proper thank you note. Even if they aren't strictly required, they will still be sent.
There certainly seems to be a lot of varied opinion on this, but I think the scribble for now would delight most of our friends and at least our close family members, so I think I will do that with her.
I'm still undecided on the goodie bags. I know a few friends would get a huge kick out of them. I'm not sure about some others.
We will not open the gifts. I think I will tape her opening presents later and if she has a particularly cute reaction to anything, I'll send the giver a little video clip to enjoy, but otherwise, we'll just stick to post-party thank yous.