Speaking geographically the best way to travel here is Naples/Positano-Rome-Bergamo-Paris/Berlin-Croatia-Athens.
Naples-Positano: rather easy and cheap. But since there is no rails in Positano, you can catch Circumvesuviana local train to Sorrento (4 EUR one way) and then bus to Positano (which is only 10km away).
Positano-Naples: use same Circumvesuviana local train or bus to Naples, from there you can already catch discounted rail tickets to Rome. Most expensive full fare EuroStar train ticket will cost you 45 EUR per person, ticket for InterCity train only 22 EUR, while for regional train only 10.5 EUR.
Rome-Bergamo: here you actually have two choices - either fly (RyanAir low cost airline has flight to Bergamo 3 times per day, for the end of April-early May it is not a problem to get a ticket for as less than 30 EUR) or use a train (in case of use of high-speed EuroStar the full fare might go up to 95 EUR, but there are still certain amount of discounted MINI offer tickets available).
Bergamo-Paris: definitely fly, since rail ticket on such short notice will cost you a fortune. Same RyanAir company has flights from as low as 7 EUR per person for late April-early May.
Paris-Berlin: again, either fly (EasyJet, Air Berlin) or try to catch discounted international ticket (not a lot of them left, but still it is possible)
Berlin-Split: similar option as above - either fly (GermanWings, TUIfly) or there is still some discounted tickets left for Berlin-Zagreb route (
http://reiseauskunft.bahn.de/bin/query.exe/en?newrequest=yes&protocol=http:&)
Split-Dubrovnik: well, your only choices here is either ferry or bus (very frequent)
Dubrovnik-Athens: hmmm... a bit complicated, but manageable. Multiple options here:
a) go by bus via Montenegro and Albania
b) by ferries via Italian Bari
c) by bus to Montenegro, then by train to Serbia and from there already catch train to Thessaloniki via FYR Macedonia
p.s. if you have other specific sequence of destinations - let us know, so we can try to get the best from your choice as well.