I don't know where to find them on the net exactly. But there is a papyrological centre in the university of Louvain (Belgium): cf. http://perswww.kuleuven.ac.be/~u0013314/cmplinks.htm
for mythographic papyri. Here you have also links to many other sites about papyri. You can aslo buy texteditions in books. There are many editions, but there isn't a big corpus of texts (like the for the Greek authors) where you can find all the texts! You can search for the Corpora Papyrorum Graecarum (not finished yet!).
You have also the Corpus dei papiri filosofici greci e latini.
And there are also collections:
-Zenon papyri (here you can find the papyrus of my anecdote, etc.)
- The Oxyrhynchus papyri ...
To find your way in these labirinth of papyri there is :
Oates - Bagnall - Willis - Worp, Checklist of Editions of Greek and Latin papyri, Ostraca and Tablets, 1992
You can browse the internet for papyri with this site http://fuzzy.arts.kuleuven.ac.be/users/jan.raeymaekers/
When you look on your left you will see: [Bronnen] and then you will also see [Papyrologische bronnen]. When you click on [Papyrologische bronnen] many links will appear for papyri on the net.
Hope I was helpful,