I have been doing this with Dropbox. I upload a character sheet in pdf, and, as I use Chrome to play, the pdf opens directly in a new tab in the browser.
The pdfs I use are fillable forms,so changes can be made during play. The only problem is that those changes can't be saved before closing, so, I still need to re-write them on the original file.
It works, but, as you see, this is not yet the perfect solution.
I thought that Mythweavers could have been a solution for saving and modifying a character sheet online, but, if you can't make your own sheet, it won't work for me.