First off everyone, she lives in California and has an 86 Cutlass. That means the car has an Oldsmobile 307, NOT a Chevy 305. Now, the biggest issue with performance that you will have is that you have the 307. There are not too many parts available for it, and to get any real gains will take internal modifications to the engine or a swap to a larger engine. The heads have ports which will not align with performance intake manifolds, and in my estimation, the K&N filter element is a waste of money. If you want to improve air flow, you will want to go with the air filter base off a HO 307 powered Cutlass 442 or
Hurst Olds. Sadly, even with more compression, a bigger cam, free-er flowing exhaust, larger catalytic converter, better gears and the dual snorkel air filter, the 442 variant of this car is a dog. It does 0-60 in 9.8 seconds according to GM literature, which is not fast at all, even by the standards of the mid 80's. So, what would I do to improve the car? I would source a larger engine and figure out how to keep it emissions compliant. The Olds 350 would be first on my list as it can be made to look stock under the hood of your car and retain the factory emissions hardware. As you face an IM 240 test and a strict visual, this may not be enough. I would speak with an Olds specialist or two in your area before spending any cash. For my money, I would build the 350 in such a way as to enhance combustion efficiency and idle quality. Put the compression at around 9.5:1 and use a head and piston combination that promotes good quench. Consider using pistons with relatively high ring lands respective to stock as this, along with the quench, will help to reduce NOX emissions (NOX emissions are sensitive to dead space in the combustion chamber and around the pistons). Use a cam with a wide lobe separation angle to reduce hydrocarbon emissions and improve low speed cylinder pressure. Remember that as you increase compression you increase efficiency up until you reach detonation. As for CO emissions, I do not remember how to reduce them in an engine build at this time.
Can you do much for your budget? Sadly, no. The best you can do is a swap to better gearing in the rear axle. Use a 3.23 or 3.42. 3.73's are a bit overboard even though they are what Olds used in the 442. The next best thing would be a swap to a 3 inch catalytic converter and an aftermarket cat back exhaust. Avoid the cat back from Dynomax as it has a poor design for the Y pipe. I think Hooker has a better one. Opt for quieter mufflers if possible to avoid run ins with the police. You will want to look for an exhaust for either a 442, Monte SS or
Grand National. The Y pipe and cat is larger in these models, so they flow better. Plus, these mods can be helpful in the future should you decide to swap the 307 for a 350.
As for how these basic mods help, let's start with the gearing. Essentially, the gear ratio is the mechanical advantage of the rear axle. Mechanical advantage is simplest to explain by thinking of a wrench. The longer the wrench, the more torque is applied to the fastener and the easier it is to turn. So, by changing gears, you increase the amount of torque seen at the wheel. With the wrench, the trade off is that you have to move the end of the longer wrench more distance to move the bolt the same distance as with a shorter wrench. With gears, it means the engine spins at a higher RPM. So, if you had to spin the engine at 1,000 RPM to go a certain speed with a 2:1 ratio, you would have to now spin it at 1,500 RPM to go the same speed if the gear ratio was 3:1. Simple, right? That is also why you don't want to go too far with the gearing in a street car. It will kill your fuel economy by spinning the engine faster than it needs to go all the time. There is more theory to it, but that's the basics. As for the other changes, They relate to air flow. A less restrictive exhaust lets the engine breathe better and climb faster through the RPM band. Why a larger engine? The 307 is hard to get to breathe due to the size of the bore which limits the size of the valves. It is a 2 valve engine, so it is limited in valve size to a total diameter of the 2 valves not to exceed the diameter of the bore of the cylinder. You need a minimum of a 4 inch bore to breathe well in most 2 valve V8 engines. This is not so in a 4 valve engine, but that is for another day.