This happens to me as well. Sometimes I also hear random disconnected sounds: a bell, pots clanging, voices, etc. There have been many nights where I've actually struggled to sleep through all the cacophony.
In "Surely you're joking, Mr Feynman", Feynman went over a few experiments he did to notice what happens when you're falling asleep when he was an undergrad. He concluded that your thoughts become more and more random and flooded as you get closer to actual sleep, until your brain gets overwhelmed and passes out.
>He concluded that your thoughts become more and more random and flooded as you get closer to actual sleep, until your brain gets overwhelmed and passes out.
At one point when I had trouble falling asleep in less than 1/2 an hour, I used the reverse to fall asleep quicker: I'd guide myself into thinking outlandish things, then my brain would naturally progress in this fashion until I fell asleep.
This has worked for me in the past. Though I can never repeat it reliably. Given enough stress for the following day, my thoughts will gravitate back to what needs to get done.
It feels the same way when I'm waking up. Whatever I'm doing in the dream seems incomprehensibly crucial, then I realize it doesn't make sense, and then that I'm dreaming, and then that I'm awake.
The most I've hallucinated while falling asleep is occasional swirly patterns. No sounds, ever. Maybe because I've had a tinnitus for as long as I can remember? (constant ~20kHz)
Likewise, nothing when waking up. Once every couple of months or so I "know" that I've been dreaming and at best can remember a person or object from the dream. After a few seconds even that is irretrievably gone.