How far off do you see the team from being a playoff team?

As always it depends on which postion we draft and if the players we draft are good.
With good drafting like REALLY good I can see us in 2018 perhaps 2017 if we dont get that many injuries and we have Alshon back + White playing great. But we would need to get a stud DE that can start, along with a starting SS/FS + CB. (Rookie of the Year good kind of players) Then we could have a chance because on paper we got a lot of good football players, but injuries have forced rookies and development player into starting. If we get all our players back healthy for the majority of the season along with new rookie stars we could reach it in 2017 but I think it's most likely that with good drafting we make it in 2018.

Getting a QB like Derek Carr would also improve the chances a lot over starting Cutler imo

I agree with that.  I would only add that a weak link in the talent-chain can limit the ceiling for an offense.  Certainly a great QB can do more than a bad QB with limited surrounding resources.  But there is a limit to what a QB can overcome.  A 2nd tier OL may be enough for a great QB to work with.  And a great OL won't make a bad QB good.  It might help a bit, but that is it.

We don't have to have a Dallas-level OL, although that would be a dream come true for me :-)

But we do need to upgrade our tackle situation, and our depth at tackle for next year.  If we wanted to really go "all in" on the OL, I would replace both starting tackles and move Leno to be a swing tackle.  I would have the interior linemen battle it out and the top-3 start, with the next guy (probably Grasu) as a high-quality backup who could play center or guard.  If you utilized free agency wisely, along with the draft, I think you could pull this off.

Who knows. As mentioned, turn arounds can be swift or stationary. I think this could be a playoff team next year- doesn't mean it will be. We could also soak in the pool of suck for years. We'll see.

Good points Jamais but an additional factor is that even a top 3 QB will not normally be ready to manage the O until after 2-3 years of tutelage in a good system.