Is there any way to know what a character's pronunciation or tone is, based on the strokes or radicals that make up the characters?
Yes, for example these characters are taken from a Chinese grammar textbook:
There are obviously others, but as you can see, it's possible to guess the pronunciation. In other cases, according to the radicals, you can understand if they refer to a certain "topic", for example, the third one in that list is the radical for "water", the last one is the radical for "fire", and so on.
too many characters can be classified into "形声字", which consists of two parts, one (the radical) indicates the topic the character is referred to and the another indicates the possible pronunciation.
xiaohouzi79 shows a good example. But remember, there are some commonly used characters that don't follow this, when you can't read a character, dictionary is your best teacher.
a counterexample is 垠（yin2），and there is a character very similar with 艮，良（liang2）