Is there a module that allows me to add files via ajax to a body field?
It is probably not exactly what you are looking for, but I'll mention them anyway, as it might give you further search directions:


plup module
Insert module
Image Resize Filter module


I like the plup module a lot, very easy to use, but based on image fields, not inline. Perhaps, in combination with the Insert module, you can get them inline. I don't like the resulting UI, as people won't understand why something so easy (putting an image inline, optionally with fixed dimensions) needs to be presented so complex.

The Media module is still thinking how to handle inline images; see the issue #1283844.