"I've come to the conclusion that devilites are by quite a margin the most dangerous enemies in the game."

I've come to the conclusion that you haven't come across a rocket puppies+greavers arena in tier 3. Either of those are a lot harder to counter than devilites, let alone both at once.

"I know of no way to dodge their attacks reliably,"

100% reliable dodge, no. But only get hit a few times over the course of a typical tier 3 Devilish Drudgery level, yes. You've got a shield. You've got legs. Use both. Keep your shield up most of the time, run back and forth across their line of fire, and attack when you have an opening.

"then please reconsider and try giving me advice instead."

All right, since you asked nicely:

There are some Sinful Steps and Ritual Road maps that have a number of devilites and kats in a small space. Certain arenas there are just hard. Other than those particular maps, devilites are pretty manageable. In particular, Devilish Drudgery maps aren't that bad.

First, you want to pull the devilites apart, so that you're only attacking one or two at a time. You nearly always have a lot of space. If there are a lot of them at once, run away fast, and see what follows. Often none will follow, so you can creep back until you're close enough that one or two sees you and comes alone.

In some cases, you don't have a lot of space to run away linearly, but can run in large circles. Do so, and devilites will slowly trail behind you. You can shoot behind you with guns, or leave bombs on the ground for them to step on as they pass.

Some maps have barriers that you can pass through and mobs can't. Take advantage of these to get away from the mobs. If they congregate just on the other side of a barrier, charge up a bomb, step just across, drop the bomb, get your shield up, and back off. They all take some damage when the bomb goes off. Repeat until most of them are dead. You have to time it right to not get hit. Right after they've all attacked, it's safe to go in, as they can't attack immediately again.

If you're only fighting one or two devilites, it should be pretty easy. One key is to note that devilites can't attack twice quickly in succession. After one attacks, it has to wait a while before it can attack again. The other is to note that normal sword attacks interrupt the "normal" devilites that can snap off attacks quickly. If you get one by itself, you can hack away until it is dead. If you have two, then if one attacks, it can't attack again immediately, so you can hit the other one, and if it tried to attack, you'll interrupt it anyway.

Magnus line guns work pretty well against devilites, as they're fast enough that devilites usually won't dodge, and the slight knockback is enough to interrupt a devilite. Piercing damage is extra effective against devilites, too.

You should keep your shield up most of the time when fighting devilites. In most cases, you attack once, then put your shield right back up. If you're using bombs, that's an exception, but no devilites should be near you.

Devilites have straight line attacks aimed right at where you were. If you run across the devilites' line of fire, they'll all miss. You can do this even while your shield is up. Run back and forth as you wait for an opening, and most of their attacks will miss, while your shield can handle the rest.

Also, get some shadow gear, especially for tier 3. If you don't have any shadow resistance, then you take about double damage. That hurts.

Pit bosses and yesmen won't attack you. You can ignore them and leave them for last. Alternatively, if you kill a pit boss, sometimes other devilites nearby get promoted to be a pit boss.

If you get down to only one type of devilite left, then all remaining devilites will turn into a hostile type. If you're leaving pit bosses and yesmen for last, then get them down to one of each before killing the last of either type.