Going over our elemental quartet, I notice the following strengths and tendencies:
[Fire] Salamanders: Lavawork, evil monologues
[Water] Ondine: Rigid hierarchies, invention, waterwork
[Earth] Gilded Gnomes: Metalwork, invention, passing fads
[Air] Fairies: Flying, small size
Given that, I'd guess the following contributions:
Food: Lots of Ondine fish farms (owing to their water affinity) and possibly Ondine regular farms (owing to their propensity for rigid work, and perhaps an affinity for egg-shaped irrigation as well). Salamanders probably supply a good deal of chef work and baking, and maybe running farms of prisoners or slaves. If fairies are gonna live in trees anyway, they might favor fruit orchards.
Industry: Gnomes and Ondine are probably both common miners, with Salamanders taking over for more volcanic tunnels. Salamanders probably also handle most of the smelting and other overt heat work, then compete with gnomes for actually shaping metal. Fairies likely supply intricate detail work. Gnomes probably dominate in working with gemstones, while Salamanders are common in pottery and glass. Harvesting and working in other raw materials is probably kind of a grab bag, while construction is probably a gnome specialty unless it involves a racial preference (towers for fairies, underwater for Ondine, being cast from lava for Salamanders).
Commerce: Gnomes are probably the big artisans and hawkers here, but anyone making things is liable to sell them. Fairies probably make the best messengers and inspectors, owing to their ability to fly and ability to fit in small spaces.
Entertainment: Gnomes cycle through fads. Salamanders produce grandiose epics. Ondine generate predictable but serviceable (if egg-obsessed) art. Fairies generate amazingly detailed work, but struggle to make it large enough to be seen by other races.