How much time Google disavow tool takes to influence on SERP

It seems to be about 2-3 days from what I can tell.

There is no time table on when it will be disavow by Google because it will take a couple of days, weeks or even months depending on the work load of the search engine.

Couple of days to months. I depends on your site solely.

The answer is not the same as it used to be. Bad links are supposedly ignored by the algorithm now, so disavowing bad links shouldn't help you at all with Penguin or any of their other "live" algorithm filters.

If you got a manual penalty, disavow links and ask for them to reconsider the manual action, however, it can take whatever time Google determines to keep that penalty in place as a punishment in order to deter you from doing it again. I've seen them remove them fairly quickly - within a few weeks - and for other sites take much longer to remove the manual action.

Keep in mind, a manual action is often taken because the algorithms are not handling the bad links the way Google thinks they should. In that case, you may never see a recovery because it was not those bad links holding the site down (they might have been helping it before the manual action). Once those are disavowed, any help they were giving the site before they were discovered with a manual action has been removed.