Car shaking and misfiring - 2001 Lexus IS 300

That's quite a collection of problems.
If the car shakes under braking, it's the brakes, not misfires. If it shakes while idling or under load, probably a misfire - to begin with, check your plug wires (particularly the socket ends at the plugs) and gapping on plugs.
Smells have a variety of causes, but usually they are related to a malfunctioning catalytic converter. Even a dead critter touching a hot part of the drive train can really stink.
Dead speedometer is usually caused by a faulty speed sensor, but your instrument panel could be faulty instead.

CHECK ENGINE MOUNTS.

Those are misfire codes 300 is multiple misfires, 301 is same but is cylinder 1, 303 is cylinder 3. This could be injectors or coil packs.

Check Engine Light On, P030x Specific-Cylinder Misfire Code A cylinder specific misfire indicates that either compression, appropriate fuel mixture, or spark is missing. Start with a visual inspection, looking for a vacuum leak near the cylinder and any sign of wear on the spark plug wire. Check the compression on the target cylinder to ensure that the engine is mechanically sound. Use a stethoscope to listen to the suspect cylinder's fuel injector. Listen for distinctive clicks and compare to another cylinder.

Misfire could be a number of things:
a) spark plugs - change them if used over 15K miles - inspect/regap.
b) spark plug wires - change them if over 15K miles - inspect
c) ECM (electronic control module) - test with HEI (high energy ignition) tester.

The shaking tells me that the engine is running on less than its normal compliment of cylinders - the shaking is produced by the imbalance caused in the engine by one (or more) cylinder(s)
not firing at all.

The "Check Engine" light probably is coming on due the the misfire condition. Go to Pep Boys or
Advance Auto Pats, where they'll tell you (free) your codes causing the "Check Engine' light to be
lit - the code coming from your truck's computer will probably be one or more of:
P0300 - Random/Multiple Cylinder misfire detected
P0301 - Cylinder 1 misfire detected
P0302 - Cylinder 2 misfire detected
P0303 - Cylinder 3 misfire detected
P0304 - Cylinder 4 misfire detected
P0305 - Cylinder 5 misfire detected
P0306 - Cylinder 6 misfire detected
P0307 - Cylinder 7 misfire detected
P0308 - Cylinder 8 misfire detected
P0313 - Misfire detected with low fuel

A misfire could be a couple of things. Due to shaking, is your car out of time? Even when a timing belt brakes, some cars can go on driving, but it would be rough like yours.

You have a spark plug or wire breaking down under pressure.I would have them changed.

When the light is blinking it means the car is actively misfiring (which is why it's shaking and running rough). When this happens, pull over immediately and shut the car off. Running with a misfire can damage the engine.

You'll need to have the computer scanned for codes - they'll tell you which cylinder(s) are misfiring. Then you can investigate. Check the spark plugs for proper gap and to make sure that the car is igniting each cylinder correctly. If you have more than one cylinder misfiring, it increases the likelihood that the coil is bad. If you're unsure of doing this work, have the car towed to a shop that you trust and have them figure out the problem.

I had the shaking problem too, had the #5 coil replaced and the shaking instantly stopped.

i need too know the engine size before i can help you