You might want to look into purchasing a Kintetsu Wide Area pass. This is a private train line that happens to have an express train that runs directly from Osaka-Namba Station to KintetsuNagoya Station. It also contains train transfers to Osaka (KIX) and Nagoya (Central Japan) airports.
http://www.japan-guide.com/e/e2357_006.htmlThe cost is about the same as a one way limited express train from Osaka to Nagoya, and one airport transfer, so it is a fairly good value.
The pass is only good for five days, and the airport transfers can be used outside of the five day period when the Pass is active. If you are flying in and out of KIX, the pass would limit your stay in Nagoya to five days, but this might work for you. It would look something like this:
April 30th: Train transfer from KIX to Nanba(Nankei) station.
May 2nd: Activate Pass, and go to Nagoya.
May 6th: Return to Osaka (Last day of the pass)
May 8th: Train transfer from Namba(Nankei) to KIX to fly home.
If you look at the area that Kintetsu train service serves, you might find other places to go, such as Nara, Ise, Tobu, Kyoto, or Iga-Ueno.
This is probably not an "everywhere you want to go" pass, but it might save you some money. It can at least be used to get you to and from the airport, and to Nagoya. I would look into an Icoca IC card to suppliment this pass. If you are planning to go several places in one day, you might also look into a day pass.
I hope this helps.