The vehicle dies when coming to a stop and or when accelerating from a stop. Upon attempting to restart the engine a strong odor of gas fills the cabin which from what I can tell enters through the Heat vents. What could be causing this?

Your problem is most likely coming from your gas cap. Your vehicle's gas cap may seem tight, but the rubber washer around the inner edge of the gas cap may be defective. Go purchase another gas cap for your car at one of the nearest auto part's location's nearest you. Change the gas cap and reset your vehicle's computer by taking the positive terminal off for a minute and replace the battery cable back on the vehicle. This method reset's your vehicle's computer. If the gas cap is the main problem, your check engine light won't come back on and your problem is solved. Gas is highly combustible and dangerous. always use precaution's when doing any work on your vehicle that require's working with any part's associated with any part's of the gas emission's system including the gas tank, gas cap, purge solenoid, charcoal canister, fuel filter, fuel pump, etc., etc. the gas smell can also be coming from a broken or faulty rubber gas line or the metal clamp's connected to the rubber hose's located between the gas tank fill valve and the gas tank itself. there are several black rubber gas hose's associated with the gas tank. have a qualified technician check the gas emission's system for any and all leak's gas also evaporate's fast, do to the combustibility again always use caution when attempting any and all repair's requiring checking the gas or emission's evaporation system. Sincerely Crystopper.

first if the cap was going bad there would be a check engine light on, system is pressurized, unless you have a check engine light, it may because you over fill it

It could be flooded with fuel. You could try pulling the fuel pump relay and cranking the engine to clear it out. A mechanic would check for spark at the plugs and also see if the plugs are fuel fouled.
Usually if the oil pressure light comes on the engine will eventually die because the fuel pump stops getting voltage.

cut off switch could still be bad. First my sure gas is getting to the engine....if so then this indicates that fuel system is working properly. Sounds like car may not be firering. Things that could cause this is coil bad, ingnition modual failed or maybe pickup coil."sensor maybe some where..timing out which would indicate timing belt or chain or gears are broke......Keep in mind these are just some things that could cause your problem and gives you ideal what to look for........hope this info helps and good luck....Please rate this post and if you need more help then fill free to contact me and we will try to get ya back on the road......

Have the catalytic converters replaced . An quit trying to play automotive mechanic , leave that to a qualified , ASE certified technician !

Sounds like the fuel pump is going out. Replace the filter first, as it's only $10. If that doesn't fix it, then it's probably the pump, which is $250.

we call these vehicles exploders.. lol
sounds like a fuel delivery issue, does it throw a check engine warning?

If the gas odor is coming from the engine, than the problem is most likely a cracked or poorly seated fuel injector.

Your timing belt could be broken. You want to have this checked as soon as possible to prevent any further engine problems.

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check for charcoal canister or evap canister full of gas