This question is directed at those individuals who actually carried a rifle into a protracted confrontation with the enemy.

Although I served, it was in the Air Force, and I have no actual combat experience. ( It has been noted that most services send the enlisted into battle, and the officers stay behind, whereas the Air Force [with a few notable exceptions] sends the officers into battle, and the enlisted members stay behind ).

I'm packing a revamped three-day emergency kit for the car, which will include an SKS rifle. Yes, I know it would be far more desirable to pack an AR or the FAL, but the SKS is expendable. If it gets stolen or confiscated, I'll be pissed-off, but not heartbroken.

Along with the rifle, I have 750 rounds of ammunition, a couple packages of stripper clips, and a basic cleaning kit. Is this sufficient?

I've seen armchair commandos recommend packing spare springs, extractors, bolts, trigger assemblies, and all manner of other spares for a semi-automatic rifle. I pretty much doubt that I'd even clean the rifle twice before the ammo was gone in a SHTF scenario.

Feedback from those with real-world experience would be appreciated.

In the military, cleaning a rifle happens often.  They get dirty and dusty while patrolling or guarding.  On the civi side of things, your rifle is far less likely to be dropped in mud, etc.  However then the threat is rust.  Make sure that the rifle is oiled or greased so it is not rusting seized shut in the trunk.

Repair? I repaired alot of Extractors, other stuff was due to damage during firefights or IEDs.

In 2003 my recon team and platoon did 70+ days in the field, in Iraq, before we did a true refit. Only cleaned when necessary and if you've carried an M4/M16 for any amount of time you know when it's needed. Example is maybe after a sand storm, a firefight or anytime you are afforded time and you think it's necessary. It's common sense really.