Take the time to go around IL. However, if you absolutely have to, unload it, empty all magazines, lock ammunition, lock firearms separate and obey ALL traffic laws. If you are pulled over, be polite but firm on your rights (4A and 5A). Do not consent to any search. If they find your firearms (and they will), they will threaten to take you to jail because you do not have a FOID card, which is impossible to get if you are not an IL resident.
926A, see also Article VI, U.S. Constitution, Supremacy Clause
http://codes.lp.findlaw.com/uscode
Section 926A. Interstate transportation of firearms
Notwithstanding any other provision of any law or any rule or
regulation of a State or any political subdivision thereof, any
person who is not otherwise prohibited by this chapter from
transporting, shipping, or receiving a firearm shall be entitled to
transport a firearm for any lawful purpose from any place where he
may lawfully possess and carry such firearm to any other place
where he may lawfully possess and carry such firearm if, during
such transportation the firearm is unloaded, and neither the
firearm nor any ammunition being transported is readily accessible
or is directly accessible from the passenger compartment of such
transporting vehicle: Provided, That in the case of a vehicle
without a compartment separate from the driver's compartment the
firearm or ammunition shall be contained in a locked container
other than the glove compartment or console.