Also open to an indirect route to Portugal via some other countries, maybe the ferry to Italy as a start?

I don't know anything about camping. I didn't like that even when I was 24. That said I have spent time in Greece. The islands are delightful, but I think you should consider some time on the Peloponnese Peninsula. The ancient sites there are outstanding and certainly give a visitor a good picture of Greek history. Nafplio is a wonderful little Greek seaside town.

Can't help you with the budget questions; it has been many years since I bummed around Greece. Your other post about Schengen visa makes me think that you will not be able to pick up work unless you are a Schengen area resident.

Perhaps you should go to the Thorn Tree forum that includes Greece, http://www.lonelyplanet.com/thorntree/forum.jspa?forumID=27&keywordid=122 as the folks on that forum are usually younger than the older farts that haunt Fodor's pages. Most of us are past the roughing it phase of our traveling days.

Your post reminded me of a book called Mani, by Patrick Leigh Fermor. He and his soon-to-be wife traveled around the fingers of land at the bottom of the Peloponnesus in the '60s, mostly by the weekly mail boat. You might enjoy it, they were exploring a region that's still not visited very much, as far as I know.

Note that July and August are peak season in Greece and even campings fill up very quickly, so it is not easy to find accommodation on the go during those months, especially after 20th July to 3rd week of August!
Free camping is not allowed by Greek law and actually there was a new low about this in Greek parliament a few months ago. That said, some islands such as Ikaria are very tolerable and welcome free camping on certain areas. Police is busy on other tasks especially on mainland, so if you go on a secluded place, it takes an angry farmer spotting you on his field to get removed, I do not think betting on this and cause disturb on local people is a nice idea though. Open fires are strictly prohibited everywhere in Greece during summer season, matter that some people seem to ignore. Campings are not so widely available as someone would think.
Furthermore, if on a strict budget, the more you move around, the more you spend. Ferries always were a bit pricey and their rates increased since last month even more, mainly due to fuel costs. Could you state an approximate budget so we could give some more specific pointers/advice?

On the mainland you can use the KTEL buses, they will get you to the most remote village of Mainland Greece, and they are not expensive at all.
Since you will be coming from Paxi island, you could start with Epirus, one of the nicest and less touristy areas of Greece.

The islands that you mentioned are located in opposite directions, Gavdos ( since Gavados doesn't exist) is south of Crete, Ikaria in the east Aegean and Skyros accessible from the island of Evia.

Best thing to do is studying a map, and find the places that interest you, keeping in mind that not all combinations of islands are possible, in terms of transportation.

If you are on a budget, and looking for less touristy places in July and August, it makes more sense to avoid the islands and concentrate on the mainland. As clausar wrote, KTEL buses are an economical way to get around, especially on the mainland. I've never travelled around northern Greece, but it seems a good place for you to look.

A recent story in Kathimerini said that Greek ferry companies have lost €1 billion over the last three years, and fuel prices are going up. That may explain why ferry tickets are more expensive this year, and timetables being reviewed.

Great, thanks so much for your responses, really appreciate the guidance!

Ferry tickets increased at 6% 1 month ago, due to the reasons that Heimdall mentioned.
A few years ago, ferry companies were allowed to sell at any price they wanted ( prices were set after negotiations with the Ministry of Mercantile Marine before this point).
The result of that was a huge increase of the prices of ferry tickets in all these years, that reduced the traffic between the mainland and the islands, as Greeks discovered that it was more economical to spend their vacations on the mainland.

The place I recall seeing camping was on Elefonissos Island at the beach. This is on the southern eastern part of Peloponnese and camping here has been going on forever.
http://www.elafonisos.info/elafonisos-camping/
http://www.tripadvisor.ca/Hotel_Review-g949051-d2237031-Reviews-Simos_Camping-Elafonisos_Peloponnese.html
http://www.simoscamping.gr/
http://www.elafonissos.gr/en/accomodation.php