This is my attempt to make sense of the legal position, mostly based on Felder's book but also some of his interviews. It's a bit long and dull, but I thought I might as well share.
Disclaimer: I'm not a lawyer and I'm outside the US but I've tried to apply some common sense and a fairly basic understanding of corporate law. It may all be wrong.
In 1980, the Eagles were owned by Eagles Ltd, a corporation with Frey, Henley and Felder as equal shareholders. Walsh and Schmit were not shareholders. All five, whether shareholders or not received an equal share of profits from performance and merchandise. Royalties from publishing came outside of this. Between them, Frey and Henley owned two thirds of the shares and therefore had a controlling interest. Of course, if Felder had been able to form an alliance with Henley, that would have changed.
In 1994, Eagles Ltd still had three shareholders. However, the proposal was to set up a new corporation for the HFO tour and record deal. All five would become shareholders but this time the shareholding would not be equal. Between them, Henley and Frey would own four sevenths of this new corporation – again, a controlling interest but just to make sure, their shares would be the only ones with voting rights. Walsh and Schmit would become shareholders for the first time and would be equal to Felder but not Frey or Henley. Note that if they'd all been given equal shares, Frey and Henley would no longer have had a controlling interest. Eagles Ltd was not dissolved and was still owned equally by Frey, Henley and Felder. Profit from earlier activities should still have gone through Eagles Ltd. Profit on the HFO tour would be distributed through the new company in proportion to the shareholdings.
When Felder was “fired” in 2001, he was offered a small amount of money for his shareholding in Eagles Ltd ($3,000?). My guess is this was based on a valuation of the tangible assets of Eagles Ltd – cash in the bank, office equipment etc – but took no account of the intangibles, the most valuable being the Eagles name (brand). The brand is used to promote records, videos, concerts and on merchandise and has potential to be used to promote a wider variety of products. How do you place a value on a name? I’m guessing that Felder’s move to dissolve Eagles Ltd was an attempt to force a valuation of all the assets.
Felder’s lawsuits had at least three components – 1) his dismissal and whether it was legal 2) the operation of the new companies (alleged sweetheart deals etc) 3) compensation for his share in Eagles Ltd. I’m only interested in the latter because there isn't much to go on for the first two. There was an undisclosed settlement in 2006/2007.
Eagles Ltd has assets that include archival material prior to 1994 and it’s been said that the release of such materials was part of the settlement deal.
Felder has hinted that he is still an owner of Eagles Ltd and makes money when the Eagle tour. My guess is that Eagles Ltd licenses the brand for new recordings, tours and for merchandise and Felder receives his share of these license fees.
I don’t think any of this affects publishing. When the Eagles play Hotel California and Those Shoes, Felder receives income from his publishing. In theory, Henley and Frey also receive publishing income when Felder plays their songs (in practice, this only happens if he has one of the top 200 US tours according to Pollstar so this is probably the first year that they’ll get anything).