In Sweden, bow hunting is illegal.......
Hunting with airguns is resticted to small game, up to magpie.
However, big bore airguns are classed the same as 22LR if they have the same power (150J/115fpe).
So, I guess that any game that You would hunt with a 22LR is fair game for a big bore airgun?
We don't have any (wild) turkeys in Sweden, but birds of similar size reguire a 22WMR and deer require a centre fire rifle (222Rem).
FX Typhoon/Logun Solo
Crosman 3540 (9mm)
Lots of Brococks......
Springfield 1911 A1 Distinguished Custom .45ACP
Smith & Wesson 29-2 .44 Rem Magnum
Smith & Wesson 24-3 3" .44 S&W Special
And a few hunting rifles....