In 1987, the caprice 305 had a 4 barrel carb with the closed loop system. At 160,000 miles, you could be facing one of a number of issues. The strong gasoline smell you mention suggests flooding. Rochester carbs from that era had a problem with wearing of the secondary metering rods, causing a fuel dump under hard accelleration. A good carb rebuild would cure this (most handy do-it-yourself-ers can do it). This course would also eliminate any problems associated with debris or sediment clogging fuel ports.
An engine with that many miles might have a slightly stretched timing chain (or worn gears) that, combined with a slightly mis-adjusted initial timing, could cause something like your problem. A partially plugged EGR valve may be the culprit, too.
Before spending any money: in a darkened garage (or at night) start the engine and let it idle. Use a spray bottle of clear water to mist the engine compartment. If you see arcing around the distributor and spark plug wires, follow the previous advice and perform a complete tune-up. You might fix it cheap. (Don't forget to replace the fuel filter
)
Have fun!