If you have industrial quantities of chemicals (more than a gallon or so), you need to call the relevant entities.
If you are lucky enough to have a hazardous waste disposal locally, obviously use that.
If you have stuff that doesn't break down well in water (cooking grease, for example), pouring that down the drain is always a recipe for trouble. You're simply going to clog your pipes. You need to dispose of that properly. There is a reason why restaurants have grease traps. Normally, residential quantities of this stuff can be placed in normal trash.
You can try to dispose of motor oil at gas stations, service stations, etc., but a lot of places won't take oil from end consumers anymore as it may be contaminated and their recycler will charge them. I actually had a very difficult time disposing of motor oil about 15 years ago. (I don't do my own oil changes anymore for this reason). I got told by the local enforcement "At the end of the day, dishwashing liquid and pour it down the toilet and the sewage treatment plant will chew it up the rest of the way." Obviously if everybody does this, it's a problem, but if it's really a one-off, it's okay-ish.
If, however, your stuff is soluble in water and you have a relatively small amount of it and your waste goes to a sewage treatment plant, pouring it down the drain while diluting it with a lot of water is often your only choice (be careful--solvents and acids can produce fairly noxious vapors even when diluted heavily) Quite often industrial disposal sites simply will not take small quantities of waste from individuals as there are liability issues involved.
Now, you may not like what even a dilute solution does to your plumbing, but that's a different issue. If your sewage doesn't go to a sewage treatment plant, but instead goes to something like a septic system, then you probably don't want to do this.
DO NOT POUR STUFF DOWN STORM DRAINS. Those normally do NOT go to sewage treatment plants (there are exceptions--but they are rare) and, as such, are a really quick way to contaminate the environment.