How close is the tornado generally when you can actually hear it?
It depends on the tornado. Of course the stronger ones will be louder and thus more audible from a greater distance, but suffice to say if you're hearing the actual tornado, you need to be paying attention because you're close. I've only truly heard one tornado, and I was .7 mile from it at the time.
And can you tell something about its strength by the sound? Or are there too many variables involved to make many judgments there? For instance, can a smaller weaker funnel have a more potent whistle to it than an actually stronger wider funnel?
Obviously any wind that's strong enough to be heard is potent, and this transitions naturally to tornadoes. Even (relatively) weak tornadoes are intense wind-wise, but compared to the wind noise of a strong or violent tornado, they are basically "mute"....but this doesn't mean they aren't audible from close range. The notion that "the louder the roar the more intense the tornado" is a safe one, but it's not the only one. There is also the notion of "the louder the roar the
closer the tornado". Knowing both is the key, and being constantly aware of your surroundings in the near-storm environment. I've only heard one tornado (which was small) so I can't compare the "roars" of small versus large tornadoes.
at what distance will you no longer be able to see a storm's top? Or does lower level cloud cover vary too much to offer much of a rule there?
In the clear sky, a few hundred miles at least. I've seen storms in southern Oklahoma from southern Kansas (DOH!). But as you mentioned, low clouds can ruin your view of a storm (not just the top but all of it in extreme cases). Fortunately, on typical Spring chase days, as the day wears on and the initial storm or storms begin to take over, the lingering cloud will eventually go away, leaving a largely-clear sky and your remaining dominating storm or storms. Once your LL clouds are gone, any storm within reach you will be able to see the top of.