Graphs search algorithms

[Xyzk]

Well to cut the story short, I`ve been (for some time now) trying to learn all most useful algorithms and how to use them. Unfortunately, our great hero was held back by magician, user of dark forces- graph search algorithms! Well, the theory is simple (as always) the problem occurs while the action is needed. How to modify them (wisely, yeah but sth more) in special cases? As an example I may give the exercise which i`ve met "find a shortest way from a to b, which total weight will be odd number. If it were find a to b i would use Dijkstra algorithm, but wht am i supposed to do here? search as long as It will find? But I`m not seeking solution. Rather than this, a book/webpage with many exercises. Yeah, I know how to use google, however nearly none of the books take into consideration the fact that I`m still a high school student :/
(for my example, right now I would probably solve it with Floyd–Warshall algorithm)

Argh.. hate to ask questions like that, feel like idiot who can`t google but I simply can`t find answer to this question.