I often hear an odd noise late at night in my house.

It sounds like it might be water draining through pipes in the walls,
e.g., running out of a sink (although it's usually when everyone else
is asleep) or going to/from hot water radiators (although I'm not sure
if I've heard the noises in the summer or not).

But I'm concerned that it could be mice or other rodents scurrying in
the walls, and sometimes I think the noise is coming from walls that I
thought had no pipes in them.

I only hear this sound very late at night, even though I live in a
very quiet neighborhood. Several other members of the household
have also heard these sounds. This has been going on for years.

Are these sounds definitely water pipes or definitely animals? And if
it's ambiguous, what is the best next step to take to find out more
information?

Just a free comment.
I think it could be the heating system.  Perhaps the water level in
the system is too low.  That is when I get a similar effect.  You
could try adjusting the valves on the radiators, turning them off
complete to see if this stops the noise.
I have found that my radiators sometimes make noise when they are
turned on full, but not, when they are turned down a bit.

I'm guessing that you have a gravity-fed hot water system. In the loft
space there will be a cold-water storage tank with a ball-float valve
on top. The ball float keeps the water level topped up, and the
hot-water cylinder is fed from this storage tank.

What happens is that during the evening you use lots of hot water, and
the ball-float valve allows the storage tank to refill. Then you stop
using hot water and go to bed. The hot water cylinder heats up the
water inside it, which expands back up the pipes into the cold-water
storage tank. This storage tank will have an overflow pipe leading
from it, and if there is enough expansion the water will reach this
level and you will hear one or more small flows of water.

If that's the case, the remedy is easy: adjust the ball-float valve so
that the water is filled to a slightly lower level. Then, any
expansion can occur without taking the water level up to the overflow
pipe.

To see if this is your problem, turn off your water heating when you
go to bed. If you still hear the noise, then your problem lies
elsewhere.

Finally, in my experience the sound made by rodents does sound like
scampering, so my guess is that you have a heating-related problem.
Heating systems are well-known for creating all kinds of noises.

Regards,
eiffel-ga

I once lived in a house that had a rodent problem. The little fellas
did make noises in the walls, but it did not sound like running water.
It sounded like running mice.

Sometimes people expect that if they have mice or rats in their house,
there will be a lot of squeaking. This notion comes from Hollywood, I
suppose. Actual wild rodents don't typically do much vocalizing. The
main noise you hear is, as well-described above by Eiffel, a
"scampering" sound. The patter of tiny feet.

I've had a rat & a mouse - but no longer thank goodness.

The rat could often be heard at night, gnawing away at something. It
didn't sound like running water.

The mouse was very quiet and we would never have known except for his
plundering of any food that was accessible.

Leave some food out ... and see if any disappears.