The 'large' ones, probably not. The 'small' ones, maybe
Is the short answer. Long answer is below:
PHB page 191 lists the the size categories, in terms of area controlled in combat, given in feet:
Tiny - 2 1/2 by 2 1/2 ft
Small - 5 by 5 ft.
Medium - 5 by 5 ft.
Large - 10 by 10 ft.
Huge - 15 by 15 ft.
Gargantuan - 20 by 20 ft. or larger
With that in mind, it's unlikely that a tiny familiar could slip under doors or through cracks in window frames.
Specifically, many Medium creatures stand between about 4' and 6' tall. As Medium, they control 5' of space around them.
It seems safe to assume that this is pretty closely related to 'wingspan', which is usually about equal to the height of a humanoid. That is to say, the widest you can stretch your arms is about equivalent to your height.
2.5' wide is 30", or about 75cm for our metric friends. That's a pretty decent idea of how tall our tiny man stands. This will define the high end of the scale -- we may have smaller creatures that will fall significantly below this.
Based off of this image from NASA, we can get a rough idea of human proportions. Unfortunately this only uses generic 'units', but it's enough to go off of.
The main thing to note is that the ratio of height to chest depth is 805:236. Applying this to our 30" height, we get something around 9".
Honestly, however, the ratio in the image seems off. Measuring in GIMP gives something more like 162:29. Using that as our ratio gives us something more like 5.4", which seems closer.
Additionally, we can run a similar ratio to try and determine how broad-shouldered our tiny man is. Unfortunately, they change around units here -- we can't directly correlate height to broadness.
What we can do is estimate the length of the torso, based on height; then compare the torso height to the broadness.
Let's say that the torso length is about 1/3 the height of the humanoid, so about 10". At a ratio of 612:378 torso:breadth, we get a rough, but workable, 6".
In short, This means we can visualize our tiny man as a box, about 30" x 6" x 6", although it's technically more of a diamond shape. There are some limitations to this model - imps aren't tiny men, and some measurements may vary.
We have some wiggle room here.
These measurements are rough -- a tiny creature could contort or deform itself (much like spelunkers) to get through narrower gaps than this would suggest. We may also be off by an inch here or there.
Even more significant -- these are based off the measurements of a tiny man.
Imps likely aren't tiny men.
They will have different measurements.
However, these give us a good idea of what order of magnitude we're working with -- the imp may vary by something like 25% in any of these measurements.
We're not deforming these too much. It seems clear that we're not squashing a tiny humanoid that's 30" tall through a 2" crack.
What about smaller things?
J.A. did mention that sprites are about 8" tall - this gives us new numbers. Let's round that to a friendly 10" tall because it it works nicely with numbers and keeps us from doing unnecessary math.
We can just divide the measurements from above by 3, giving us something like 10" x 2" x 2".
For creatures under a foot in size, it's plausible that they could slip beneath the gaps in rougher-hewn doorways.
Still probably not the windows, though.