Cylinders 2, 4, 6

It just can't do that. No way to shut down one side of an engine.
Misfires are caused by lack of fuel, spark, or compression. One of the three is missing. One whole side-that rules out spark. Coil pack design just won't affect one side of the engine. That leaves fuel or compression. Some multi-port injection systems are so-called "bank fired" -that is, one side or bank of the engine will pulse the injectors at the same time, first one bank, then the other. But in the early '90's, some cars came out with sequential fuel injection, which pulses the injectors individually, following the firing order of the cylinders, more precise fuel metering that way. I would have thought that an Avalon would be sequential injection, but you could check. Anyway, you need to check if the injectors are working on 2, 4, & 6. The power wire to all injector systems is a single wire that is spliced to each injector. Conceivably, the splice to that bank or side may have broken. With key on, every injector should have voltage at the injector connector. Only two wires to each injector- a power wire and a ground wire. If no power on 2, 4, or 6-that is probably it. (On bank fired injection, all three ground wires on each side splice together before the ground wire goes into the computer. With sequential, each injector ground wire goes to the computer separately.)
Beyond fuel, it is possible that the fuel/air mixture is being affected on only one side. If you have a noisy exhaust leak on that side, it could lean out the mixture.
Finally, low compression will cause a misfire. Possibly, a camshaft on that side is not in time. Only way to check is to do an engine compression test.

Did you mix up the plug wires when you replaced the spark plugs?

Check the fuel injectors

Is the coil plug on the right order something like 1 3 2 4 and so on try it