This is a chapter book that I would have read in the early/mid 2000s, though I suspect it was published closer to the 90s or late 80s as it wasn't new when I read it. It was given to me as a kid's book, and it was fairly short, but given some of the subject matter I suspect it would be sold as YA if it were released today. It's set in the real world, and is sort of a sf/f fusion - the sludge is explained by science, but some elements of its creation felt very fantasy-like. The cover was illustrated and looked very 'pulpy'; I remember it depicted a boy standing in glowing green slime with a shocked expression on his face. I read it in the US, and I believe that it was probably written in English by a US author.
The basic plot is that a teenage boy is on a family trip to his grandmother's cabin for a big summer reunion. He's very unhappy about this, as he doesn't like most of his family. The only people he's really interested in are his grandmother, a drunken batty eccentric who brews her own moonshine, and his beautiful cousin who's his age and will be going to college soon. (He also has another cousin the same age, a closed-off girl he doesn't pay much attention to, who ends up a crucial character.) While there, he decides to borrow an old bike to take a ride around the lake - however, his brakes fail and he ends up falling into a pile of gross lake sludge filled with chemicals left behind by a company that used to dump them there years before.
After falling in this, he slowly realizes he's beginning to develop psychic powers, foremost among them reading minds. With this power, he begins to understand that most of his family - excepting his grandmother, who really is just a batty eccentric - are much different than he saw them before. He realizes that the beautiful cousin he liked so much is actually shallow and cruel to others, but the quiet one he ignored has a rich inner life and is very clever; he ends up explaining his secret to the second girl and enlisting her help in trying to understand the limits of his powers. In return, he helps her get out from the influence of his cruel cousin.
However, his cruel cousin ends up getting dosed by the sludge too, even more than the boy did, and ends up using her newfound powers to manipulate and break the rest of the family.
I forget exactly how this happens, but the grandma - who's oblivious to this all, her addled mind being too slippery for the cousin to mess with - offers all three of them drinks. The boy and the good cousin get beer, the evil cousin gets soda. When drinking the beer, the boy realizes that his abilities are suddenly increasing at an incredible rate; he and the good cousin become easily able to to overpower the evil cousin, and are even able to do things like read the minds of everyone in a plane thousands of feet above them. The boy pokes at his grandmother's mind once more - and the 'simple' mental landscape falls away. She draws him into her now-infinitely-complex mental landscape, and reveals that she knew the secret of the sludge all along. The moonshine she brews is made with the sludgewater; her drinking it for all these years has given her near-godlike mental powers. Everything that happened - both the boy and the cousin falling in, the mental battle - was masterminded by her to determine who should become her heir to the 'throne' of psychic powers now that she's growing old, and she's decided she wants the boy and the good cousin to be those heirs.
Some other notes:
- The grandmother's 'true' mind was described as a strange, dusty factory filled with eerie spider-like robots.
- The boy learns mental shielding, first on his own by experimentation, and then from his grandmother. His grandmother's mental shielding is so complex that he even by the end of the book he barely comes close to understanding it.
- The cruel cousin is blackmailing the good cousin by threatening to reveal to the rest of the family that she cheated on her college entrance exam.
- The book, despite the seeming silliness of the plot, had a very eerie and strange tone as I remember it. In particular, the idea that someone you think you know could turn out to be a complete stranger was given a lot of weight.
- I think the boy and the good cousin ended up a couple? It was definitely set in the US, so I found that a bit unusual, but I don't remember the potential taboo there being remarked on much.
- The main characters are juniors or seniors in high school, preparing to go to college soon.
I don't think the title had the words slime or ooze or sludge in it, if that helps.