We are planning on travelling around poland and possibly some other eastern european countries for a month or so in June. Does anyone have any advice as to how we can do this for as little money as possible?

And also how to reach Poland from Stockholm?

Hi there, firstly I would recommend that you check out for cheap flights with any of the discount compaies, ryan air, sky Europe and so on.
Then in Eastern Europe, I would definitely not restrict yourself to Poland, although that is a cool country. In Poland I think that you should really try to visit Krakow.
If you can then go to Slovakia too, and visit Kosice, Spissky Nova Ves and maybe the Tatra mountains if you like trekking.
If you are interested in going to the Czech Republic then head to Ceske Krumlov or Ceske Budejovice as Prague will be heaving at that time of the year. Anyway have fun.