Unloaded, and in a case.
(Ammo can be IN the magazine, as long as the magazine is not in the gun)
CASE is defined as a closed container - for the purposes of the definition, the IL supreme court ruled that your car's center console or glove box IS a firearms case, IF it latches. Doesn't have to lock; just has to LATCH.
I keep (depending on mood) an unloaded 9mm or 357 in the center console of my Mustang, with either 1x17 round magazine or 2x5 round speedloaders laying next to it.
Also by definition, a disassembled firearm needs no case. It's no longer a firearm.
So if you arrive at the Illinois border on a motorcycle carrying a loaded handgun...
Take the magazine (or ammo) out, put it in one pocket. Take the slide off (or remove the cylinder) and shove it in a jacket pocket.
I've ridden to the shooting range before with an AK-47 slung across my back, bolt in my pants pocket.
Get some funny looks.
But a firearm "broken down in to a non-functional state" is no longer a firearm, per IL law, and not subject to the Unlawful Use of Weapons laws.
(Which were struck down anyway as unconstitutional, but that doesn't go in to effect for another 56 days.)