Besides Token Eastern Song from the 9/89 Blew EP sessions with Steve Fisk, In his hands from the Nevermind sessions and You've got no right from the January '94 Bob Lang Studios sessions, there could be some unheard studio material. Besides Kurt's own demos, of course. There is the infamous Fecal Matter demo from 1985, Kurt's March 1994 demo (with the much sought-after Me & My IV), the fall '90 4-track demos and other stuff. Just up until mid-'97 no one knew of Old Age. The full song is probably also going to be on the album. The book Come as you are says Kurt had a couple of more songs during the time of the recording of Nevermind, which were melodic and a bit "softer" than the material put out on Nevermind. This could refer to, at least, In his hands and Old Age.
And we can't forget about the early '93 Nighty Nite demos, done by Kurt, Courtney and Patty Scheimel in Seattle. There we have more songs, but they can't really (in my opinion) be counted as Nirvana songs. Kurt was the only Nirvana member present.
Another Kurt/Courtney collaboration is the tape they recorded while in Brazil, in January 1993. From this demo we have "Closing Time" and "Determined" so far, but there were probably more songs recorded.
During the rehersals for the MTV Video Music Awards on Sep 9th 1992 the band played, according to CAYA, Rape Me, and a song provisionally titled "New Poopy". This is thougt to be tourette's, which (as we know) was debuted on 8/30/92, then named "The Eagle Has Landed". The version on the bootleg Shoot the Shit vol. 3 is fake, it's not Nirvana.
On page 69 in CAYA there is a picture of an early setlist. On the reserve list there is a song named "Vendetagainst" stated. Two fake versions of this song are on Shoot the Shit vol. 3, cleverly named Vendettagainst and Vendettagainst '88. Right before Spank Thru on 2/9/90 someone in the audience shouts "Vendettagainst!", so this song might pop up on some recording soon.
During the Jan '94 sessions they recorded, as mentioned before, You've got no right. Krist and Dave also demoed/tried out three more songs, two of Dave's and one of Krist's. One of the songs demoed was the to-be Foo Fighters song "Exhausted". In March 1994 Kurt re-recorded some older stuff, and also recorded a new song, "Dough, Ray and Me", which would be his last.
Another of the "melodic" songs left over from the Nevermind recording is a song known only as "Song in D". To me it sounds like it's vocalless, or perhaps has only rough vocals. It had never been heard of until the release, in late '98, of the book "Classic Rock Albums: Nevermind", on the making of Nevermind. I don't know if this will be on the new album.
Dave once said in an interview that Nirvana used to play one of his songs during soundchecks for European 1991 shows. This was unknown up until mid-'98, when Rob Holmes found out it was the to-be Foo Fighter song "Alone+Easy Target".
Many hope that there are more unheard, unreleased Nirvana songs. I've read interviews where Dave and Krist say that "there's enough unreleased Nirvana material to put out another album". And that's what we all are waiting for.