The term which is used for illogical is irrational, referring to something done or said without reasoning. Other terms that may work depending on context are unreasonable, ill advised, rash, thoughtless, heedless, reckless.
yes
He was illogical in his thinking.
Not that your suggestion seems illogical, but the term used IS trompe l'oeil.
It's called illogical extrapolation.
Highly Illogical was created in 1993.
The Illogical Consequence was created in 2005.
the processes that are not logical are called illogical processes
who said this atoms of different elements are different
The way that he answer the questions was very illogical.
the logic in being illogical is the logic that the illogicality can be logically answered by any logical person with logic on illogical logic.
In Japanese the term Makezu Girai, is an illogical compound that means "make-girai" or "hating to lose."
I'm pretty sure that Mr. Spock would say that that is illogical. The illogical strategies really are not so random, after all.