I was actually in the middle of writing Mecha lore for the tournament, guess I'll finish that later.
Right, so right off the bat sickness and radiation are completely ineffective due to Mecha's inorganic body, vacuuming probably just wouldn't be used since Mecha's pretty big himself, (And if it did happen, a chaos blast there and Plague Demon just dies) Plague Demon's attacks softening an afflicted person's body might work, though reading through one of his last matches it also sounded like it still needed to infect the person to actually do so? Regardless, if it does work, then Mecha would realize pretty quickly and likely avoid close range combat where he'd be more vulnerable, especially since he wouldn't even be able to make contact without being afflicted (Though said weakening can be somewhat countered by chaos emerald amping, in fact, said weakening would actually likely prompt Mecha to use the emeralds sooner than he would have otherwise) in terms of stats, Plague Demon's profile isn't helpful, but according to his last match, he's relative to Knuckles in AP, who's 39 Kilotons, while Mecha Sonic is >28 kilotons, so Plague Demon is likely a bit stronger, meaning material weakening could actually leave Mecha pretty vulnerable. That being said, info analysis means Mecha should be at least aware of the fact that close range combat is a bad idea, and Mecha's got no shortage of ranged options, with his energy blasts outranging even plague boost's farthest reach, teleportation to make sure he stays out of the way of any major hits (What exactly does the "dark aura" do?), flight granting vastly superior mobility, and with the emerald amping greatly increasing his speed (Though he probably wouldn't be full on blitzing due to plague boost increasing Plague Demon's speed as well, he'd still be quite a bit faster) and light speed attack to further increase the gap, a game of keep away would definitely fall in his favor, and Mecha falling back to ranged combat means he'd also be out of range of Plague Demon's slowing aura. Likewise, Plague Demon getting in cqc range isn't an instant death sentence for Mecha, at that range Chaos Blast is liable to do major damage (Plague Demon is only ~1.4x stronger, both are probably being amped at that point, though Mecha's boost sounds more impressive, being able to stomp comparable opponents while plague boost is only described as a "slight boost to all his stats" in his P&A section, so the gap at that point is practically nonexistent, and with chaos blast being able to completely obliterate several clones of Tricky who were comparable to Mecha, it'd probably come very close, if not outright take Plague Demon out if that happens), and while Mecha would be in range of the slowing aura at this point, he'd likely be emerald amped, which would cancel the speed reduction out, so Mecha would be able to reliably get a chaos blast off in that situation. In terms of stamina, while Plague Demon's is effectively limitless, Mecha's feat of genocoding an entire planet means a war of attrition wouldn't turn in PD's favor, even if he could theoretically outlast Mecha, the latter's stamina is vast enough that he'd be able to reliably kill PD before it became an issue.