Unreleased but available:
"Celebration," written by Spike Edney, recorded by The Cross sometime around or shortly after the Shove It album sessions.
"I Can't Get You Out Of My Head," written by Clayton Moss, recorded by The Cross probably during the Mad, Bad And Dangerous To Know sessions (if I had to guess).
Both were previously believed to be Roger solo tracks from the Stranger Frontier era, but Clayton Moss set the record straight via his website/Youtube site.
Those are the only two I know of definitely unreleased but floating around the internet. Other unreleased tracks hinted at include:
"Let's Get Drunk And Be Somebody" written by Clayton Moss. It was performed live during the Shove It tour and later recorded for Moss's solo album The Cross Section, so there's a chance The Cross recorded a studio version at some point. No specific evidence, though, just a guess.
"Dear Mr. Murdoch" was reportedly aCross track from the Blue Rock sessions originally, which Roger recorded later for his solo album 'Happiness?'
According to an interview with The Cross promoting Blue Rock, they say they recorded something like 30 songs for the album, had their producer pick the best 10 and those 10 are what is on the album. Of the remaining 20, one could be "Dear Mr. Murdoch" and one is very certainly "Heartland," the non-album B-side of the withdrawn "Life Changes" CD single.
Other songs The Cross *might* have recorded at some point include songs which have appeared on various solo projects since (by Roger, Clayton Moss and SAS Band):
The SAS Band's first album includes a version of "Dirty Mind," and another Edney-penned song "Dreamworld".
Clayton Moss's solo album The Cross Section features five Cross songs: "Penetration Guru," "Ain't Put Nothing Down," "Better Things," "Let's Get Drunk And Be Somebody" and "I Can't Get You Out Of My Head." The remaining two songs "The River" and "Days Without You" might (maybe...I don't know) have been recorded by The Cross. We know "...Out Of My Head " was, but beyond that it's pure speculation.
Lastly, maybe any of Roger's songs recorded since their break up could date from The Cross days. He did re-record "Final Destination" (and possibly "Dear Mr. Murdoch" is a re-record) for 'Happiness?,' so...maybe...could be? I really have no answer beyond that.
Hope that helps. Did I miss anything?