What happens between EP3 and EP4?

I know ill probably get slack for this but wouldnt you agree that theres a bit of information in between episode 3 and episode 4

for instance how does leia know obi-wan, and how come he doesnt recognize the droids in EP4?

I believe in a few years you will have more than enough answers as I'm sure there will be numerous books covering this era

Between Episode III & Episode IV?
Here's what we "know":
-Darth Vader hunts down the rest of the Jedi & remaining Force Users.
-Leia Organa is raised by her "father" Bail Organa, who tells her remarkable stories about the long dead Jedi Order - probably including tales about Obi-Wan Kenobi.
-Luke Skywalker is raised on Tatooine by his Uncle Own & Aunt Beru, helping them harvest produce from the moisture vaporators. He watches many friends go away and join the Empire, (most just going to the "Academy", more akin to Colleges and Universities rather than militarism).
-Yoda goes a little insane on Dagobah. 😛
-Obi-Wan becomes an eccentric old man, a local Tatooine legend.
-Etc.

I wonder how many Jedi are left alive after ep. III?

Few, but there are some.
And many aren't even Jedi, but people who would've become Jedi had the Order found them....

Maybe Obi-wan doesn't recall the droids because he has gone slightly senile?

yea thats gonna be a tricky one for lucas with the droids he just had to p[ut ot characthers in the pt, well this is what he gets

Obi-want has hardly any contact with 3p0 or artoo in the prequals, he also never owned a droid, only borrowed a couple of R4 units from the jedi.

there is a new series set shortly after E3 where obi-wan hears rumors about left over jedi and tries to find them, plus there is the coruscant nights trilogy and The Dark Lord (picks up where E3 leaves off).

One of the aforementioned series' is done by Michael Reaves....😉