This tour has been widely covered both by photographs and some videos, as well as the band's first biography which came out in 1976 and listed Roger's drum set in detail. In July/August 1975, John stripped off his 1965 bass and left it natural, but he didn't do the same with the other yet: a Fan Club magazine from late 90's reveals a photo from the band performing in Australia (and it's definitely this tour as confirmed by the logo of Roger's bass-drum) and John's using the 1968 bass, which at that point is still sunburst.
Tony Iommi from Black Sabbath recommended Brian to commision John Birch to make a replica of the Red Special, which he did. Brian used it as his spare guitar from late 1975 to August 1982, when he smashed it one night he was particularly upset.
Gong [hit once at the end of Bohemian Rhapsody and Ogre Battle]
Triangle [Killer Queen]
Guitars / banjo
Electric six-string guitars
Ukelele-banjo [Leroy Brown]
Electric bass guitars
What about the recording sessions?
Freddie used the white Bechstein IV piano for the rehearsals and possibly for most of the recordings as well (notable exception: Seaside Rendezvous, where it's a Yamaha C-7). Brian possibly used the Birch guitar for at least some of the overdubs on The Prophet's Song, on which he also played a Tokai Hummingbird six-string acoustic (also Love of My Life). John Deacon played Wurlitzer EP-200 electric piano on You're My Best Friend and he might have used a celeste (unknown brand) for the bell-like overdubs. The twelve-string acoustic Brian played on '39 is most likely an Ovation Pacemaker 1615. There are some photos of him rehearsing with a Baldwin Bison, but it's unknown if he also used it for the record.