@kcdude That's a good page, but it doesn't tell you much about the idiomatic use of the word, which I think is the crux of the issue.
"And also" is grammatically correct, but not idiomatically; if you're not familiar with the word "idiom" or "idiomatically," well, it's kind of vague, but it basically means "in common use." If you say something that is grammatically correct but "sounds wrong," it's probably not idiomatically correct.
"I like TV and radio" or "I like both TV and radio" would be the typical way to phrase that sentence. "Also" can imply that you forgot something ("I need to take out the trash first. Also, I need to do the laundry."), like a verbal version of a P.S. (post-script) in a letter. It can imply that something is attributed to something else unexpectedly ("This blender also acts as an egg-beater!"). These are typical uses of the word "also" in colloquial English. "And also" is redundant, because both "and" and "also" mean the same thing in this context. You could say "I like TV, also radio" if you wanted, although I'm not sure if that's grammatically correct.