What is an appropriate proverb or expression that means one has:
- Taken on too many tasks
- Set out to do something that one isn't qualified to do and hence probably will fail
- Set out to do something that probably is impossible to begin with
For doing something that is too hard, or doing too much of it at one time, I'd say you could go with
Biting off more than he/she can chew
which usually implies "taking on too much/too may tasks", but I think it's fair to stretch it to "taking on a task that's too hard for you". This is, to me, the most obvious idiom for this, but it's fairly cliche.
You could also use
Getting in over his/her head (as in, the water is too deep)
which implies swimming somewhere where your feet can't reach the bottom, and yet you're not a strong enough swimmer to handle it. You can also use
He's out of his depth/He's in too deep
which is the same metaphor. Neither of these imply failure, since the speaker may have misjudged the swimmer/chewer. I can't think of a phrase that combines these with the notion that the task is impossible; usually impossible tasks are impossible for everyone and not just for one person (swimming in deep water may be impossible for him, in which case he's getting in over his head, but it's not impossible for me, in which case I just swim there).
I really like Mr. Shiny's answer, and I almost just made this a comment there, but I suppose it deserves its own answer.
You can say that someone is engaged in a Herculean task. When used alone, the word herculean implies great strength, but an Herculean task connotes "requiring tremendous effort, strength, etc.", in reference to the seemingly impossible labors that were required of Hercules in Greek Mythology.
Because Hercules succeeded in his labors, this idiom wouldn't go quite as far as to say that the task is utterly impossible--only that you'd have to be on par with a demigod to accomplish it.
Along the same lines, but with a stronger emphasis on failure, the American Heritage Cultural Dictionary has the following note on the definition for Sisyphus:
A difficult and futile endeavor may be called a “labor of Sisyphus” or a “Sisyphean task.”
Either of these phrases requires at least a cursory knowledge of Greek Mythology, so they may not be appropriate for your audience, but saying that someone is engaged in a Sisyphean task seems to match your criteria well.
The only one not yet mentioned:
Too much on her plate.
Implies overcommitment and a lack of spare time.
You have listed very specific criteria, and unfortunately, I doubt if there is actually one single idiom to describe all of that. One could possibly use a combination.
For "doing too much" :
Burn the candle at both ends.
Bite off more than he can chew
Carrying it too far.
For "illegal" :
You'll be caught red-handed
Taking the law into his own hands.
Flogging a dead horse. Nailing jelly to a wall
I would suggest, if you were to want a sentence expressing all three of your criteria, something like this:
You can't catch lightning in a bottle(impossible), besides, you'd probably be caught red-handed(illegal), and end up trying to burn the candle at both ends(do too much)
For "taking on too many tasks", I suggest spread oneself too thin or stretch oneself too thin. Its definition is:
To work on too many projects: overextend oneself.
A task that is beyond one's abilities can be likened to shovelling sand with a teaspoon, or, while we're at the beach, trying to empty the sea with a bucket. These are the only metaphors based on common experience, rather than classical mythology, that come to mind right now.
Augean task adjective Etymology: Latin Augeas, king of Elis, from Greek Augeias; from the legend that his stable, left neglected for 30 years, was finally cleaned by Hercules Date: 1599 extremely formidable or difficult and occasionally distasteful
As I always told my smartest students,
A common phrase for either taking on too many tasks at once or taking on something that's too difficult is biting off more than you can chew. I don't think there's an existing common phrase for taking on a task that's impossible. (You might just say "He's attempting the impossible" or "trying to do the impossible")
"Spread yourself too thin."
to try to do too many things at the same time, so that you cannot give enough time or attention to any of them:
For taking on too many tasks, you could describe having "too many irons in the fire"
William Shakespeare, Macbeth:
Life; is a tale told by an idiot, full of sound and fury, signifying nothing.
Given somekind of context, you could alter and say:
Life; is a tale and your an idiot, you fail to see the sound of fury, you signifying nothing.
Alternatively, from Confucius:
The hardest thing of all is to find a black cat in a dark room, especially if there is no cat.
I think these may all work for: