Do we have any information about when the war started? IIRC, the Great War was about/at least 30 years before the events of Skyrim, and at some point in that time (or soon after) the Markarth Incident occurred, and Ulfric was imprisoned for a time (during which his father died), and eventually got out. Then he would have had to get back to Windhelm and gather power, and finally kill Torygg, and the fighting came soon after.

I can't remember anywhere that specific dates or lengths of time are mentioned. I'm a little confused, because some dialogue makes it sound like the war hasn't been on for too long, while other lines imply (to me, at least), that the war has been dragging on for a long time.

Is there any reference for the date of the Markarth Incident, the duration of Ulfric's imprisonment, and the beginning of open fighting between rebels and Legionaires? Or at least how long the war had been on at the time of Ulfric's capture and near-execution? I know Hadvar mentions Tulius' arrival being relatively recent.
If the information's not there, what are your estimates?

The rebellion seems to have been going fairly soon after the Markarth incident. The war itself has been going on for a year at most I'd say. Someone saying they're a stormcloak doesn't necessarily mean wartime stormcloak. The rebellion group in Skyrim was called Stormcloaks far before Ulfric put his support behind it.

The date of the Markarth incident is 4e176. The rebellion happening the same year or the one after.(Igmund mentions that the stormcloak rebellion started in Markarth. It's possible Ulfric's "We're not going to stop worshipping Talos just because the elves say we have to. We had a deal" group's surviving members that weren't imprisoned were the original rebellion founders.) They were the original ones that attacked imperial groups and such. In an effort to quell rebellious sentiment, "Bear of Markarth" is written to discredit the movement. The war itself started with Torygg's death, and I'd assume it's rather recent. A year at most I'd guess. Roggvir's still alive after all.

Edit: Ulfric's definitely been supporting the stormcloaks longer than a year, and the war in full has only been going on a few months.(There had been skirmishes before though. One ex soldier notes a skirmish near windhelm several years back)

"Ulfric founded the Stormcloaks years ago, as a sort of private army to advance his ambitions. He's always used the ban on the worship of Talos to stir people up against the Empire. He never succeeded in getting much support, so a few months ago he murdered the High King!"

Either the empire didn't know Ulfric was behind the stormcloaks, or Ulfric had never publicly ordered them to attack Imperials. His trip to Solitude wouldn't have happened if he was already considered a traitor given all the imperial presence there.