Nay, the Impire is as strong as any other faction, in fact still stronger than most, which is why it's wise to side with the empire. You can't blame the empire as a whole because of a few rotten apples. The stormcloaks have their fair share of ignorant individuals. The true enemy is the Aldmeri Dominian, and they are strong. They love the fact that there is a civil war among the humans. Ulfric picked a rather bad time to wage his self righteous war against the empire when the Aldmeri are ready for a second strike against HUMANS. The empire has the most resources and ability to fight off the high elves, and that's why these stormcloaks must be crushed quickly if they can't come to their senses.
The Empire is about as strong as the finger Ulfric flipped them while he rode out of Solitude. The Empire has to rely on local recruiting from within the Skyrim population to bolster their forces to quell a rebellion that is extremely selective in it's recruiting (racially and honor-wise). If the Empire hasn't brought down an insurrection by now with their so-called "strength" you claim they have, then Man is doomed to serve Mer.
You can blame the Emperor wholly though, and thus the Empire, as he represents it. He is the one that started the chain reaction of [censored] hitting the fan when he gave in and signed the WGC when the Dominion was nearly fought to a stand-still.
They do love the fact that a civil war is taking place, mostly because, in my opinion, they are not NEARLY as powerful as they let on as they were severely weakened in the Great War too, not to mention it takes them far longer to build a military force capable of withstanding human-capable numbers (who spawn like rabbits compared to Mer because of the maturing rate that coincides with their very long lives), giving humans the advantage of numbers before you even take into account that the Altmer are extremely selective in their breeding and it takes a fat minute to match suitable mates that will produce "worthy Altmer" in the eyes of the Thalmor.
Like I said above, the Dominion is most certainly in a weakened state and is in no way, shape, or form able to launch another invasion on the Imperial City. Alongside their vastly reduced military, you can bet your ass that the Empire is extremely vigilant when it comes to their borders now (they jumped you crossing the border, a single person), removing the only deciding advantage the Dominion had over the Empire at the time -- the element of surprise.
The Empire's basic resources of war:
1. Silver from Markarth (wealth), which is slipping away in the war. --Possibly Gone
2. Fish and Honey from Riften (sustenance), which is now under Stormcloak control unless you trade it away or fight for the Empire to take it. --Possibly Gone
3. 1/2 of their Nord soldiers, which has sided with Ulfric in the Civil War. These soldiers are skilled sailors as well as an invaluable vanguard to any army. --Half-Gone
4. Ebony from Morrowind, which is now annexed by Argonia, an independent state from the Empire and thus is under foreign control. --Gone
5. Soldiers from Morrowind --Gone
6. Soldiers from Black Marsh --Gone (Neutral)
7. Soldiers from Elswehr --Gone (Neutral)
8. Bosmer archers, which are the finest in Tamriel --Gone (Enemies)
9. Altmer mages, the most effective crowd-control artillery-esque units Tamriel has --Gone (Enemies)
10. Redguard foot soldiers, who are the best "jack-of-all-trades" warriors in Tamriel --Gone (Forsaken to the wrath of the Thalmor)
11. Breton mages, who are the only non-Altmer mages that are on par with them; primarily defensive instead of offensive though. --Unknown (Blocked from Cyrodiil)
12. Orsimer berserkers, the finest warrior shock-troops the Empire can get --Unknown (Also blocked)
As you can see, the Empire doesn't exactly have the resources you boast about. Not the kind it needs anyway. The stormcloaks are obviously feared by the Thalmor, as they don't want them to win the war either.