I agree with the marked answer and would like to add on a few points.
Yes, there were more pressing issues at that time but also:
- Neither Harry nor anyone else report any of those illegal actions. When Umbridge used the blood quill on Harry, he "didn't want to tell this incident to Dumbledore since he was preoccupied with a lot of other, more important things"
- Moreover, Umbridge was sent to Hogwarts by the ministry of magic to do just that. The minister of magic, Cornelius Fudge, did not want to believe that Voldermort had returned which both Dumbledore and Harry claimed. As per Fudge, this was a conspiracy to overthrow the minister. So safe to say, no one would believe or help Harry to punish Umbridge from Ministry of Magic.
- Even when Umbridge threatened to use the cruciatus curse on Harry she said "What Cornelius doesn't know won't hurt him".
All this, and the reason that Harry and Hermoine were being tortured and pushed to give up the secret weapon of the order of the phoenix, was probably why they took the matters into their own hands and handed her over to Grawp and the Centaurs in the forbidden forest.
Why was she not arrested after Dumbledore came back and Umbridge
resumed her job at Ministry of Magic ?
- Umbridge was "a woman of power", so she obviously had connections in the Ministry (she directly reported to the Minister of Magic).
- By the time she was back in power after her time "teaching" at Hogwarts, the Ministry had almost already been infiltrated by Death Eaters and/or Voldemort supporters and spies. She wasn't necessarily part of that crowd, but they were more into the idea of chaos and darkness (ie: Dementors and torture) enough to possibly overlook anything wrong with what she did.
As to why, they didn't complain to Dumbledore regarding what had happened, they probably thought(speculation?) what happened to Umbridge at the end of OOTP was a suffice punishment since they didn't seem to worry about her after that and headed straight to the ministry. And, even Dumbledore wouldn't have been able to punish Umbridge without the Ministry of Magic's involvement.