I think “overwhelmed by” reflects the emotional state of the victims. That is, they felt overwhelmed. Alternatively, they might be __disheartened__ by the amount of work.

“Overwhelmed with,” on the other hand, seems more to deal with the state of __things__. That is, the volume of work would not fit into the container available for it (time or space.) Alternatively, the work might __exceed the capacity__ they had to get it done.

As @6rant6 has started to point out, the differences between “by” and “with” in your first examples are pretty subtle. As an English reader I’d read being “overwhelmed with” work to be a temporary overload of “tasks to be completed as part of one’s job in the near future”. In other words, someone has dumped an unusually large quantity of “work” on you, and now you have to do that work. On the other hand, I’d read “overwhelmed by” work as a more chronic condition: that one is incapable of doing the job, doesn’t have the resources or training, can’t work with the people, is oppressed by the environment, etc.

So my reading is that “with” in this sense represents an acute condition, and “by” is more chronic and (probably) more onerous. Maybe that’s just my reading.

I wouldn’t use overwhelm as an active verb in this case. “Work” does not overwhelm a person, although it’s possible for a person to feel “overwhelmed with/by” work (there’s nothing wrong with those sentences).

On the other hand, “things” can overwhelm people: the wave overwhelmed the boat; the storm overwhelmed the campers; the white-water river overwhelmed the canoe. But the difference is that those are physical cases of “overwhelm”, where the active voice is certainly apt.

Humans can overwhelm other humans, too, of course. Armies overwhelm other armies from time to time.

As to your question regarding adjective/passive voice, overwhelmed by and overwhelmed with are verb phrases, so it would be passive voice.

I am curious as to your interest in the distinction between adjective and passive voice. Is this for a test? It is not something that most native speakers would think about.

@CWOTUS : Simply nailed it down! Now, understood the meaning of it. Thanks!.
@6rant6 :Thanks for the explanation.
@LostInParadise : No. It wasn’t for a test. I just had a look on this Wiki article. I could not recognize passive and past participle adjective sentences very quickly. I get confused when any verb is used with Be + verb structure(If it’s not followed by By, usually in passives).

Did you ever notice people are either overwhelmed or underwhelmed? No one is ever just whelmed.