1Unreasonable; unjustifiable; also used to mean impossible or impractical depending on context.
そんな条件は無理だよ、交渉のしようがない。
Those conditions are unreasonable; there's no way to negotiate.
彼の提案は無理があると思う。
I think his proposal has unreasonable aspects.
無理な要求を断るのは大事だ。
It's important to refuse unreasonable demands.
2Impossible; cannot be done in practice or reality.
明日までにこれを全部終わらせるのは無理だ。
It's impossible to finish all this by tomorrow.
一人で40箱を運ぶのは無理だ。
It's impossible for one person to carry 40 boxes.
彼を説得して来させるのは無理だろう。
It will probably be impossible to persuade him to come.
3Forcible or forced — done by compulsion, usually used adverbially as 無理に.
荷物を無理に押し込んだら壊れてしまった。
When I forced the luggage in, it got damaged.
彼は無理に会話を続けようとした。
He tried to force the conversation to continue.
4Excessive; immoderate — describes overwork or unreasonable burden.
毎日の無理な残業で体を壊した。
I ruined my health with daily excessive overtime.
無理なダイエットは健康に悪い。
An excessive diet is bad for your health.
5Usually expressed as 無理をする, meaning to push oneself beyond one's limits or place excessive strain on body and mind.
体調が悪いのに無理をして出社した。
Even though I felt unwell, I forced myself to go to work.
無理をすると後で後悔するよ。
If you overdo it, you'll regret it later.
6A colloquial interjection meaning "no way" or "not a chance" — used to strongly refuse or deny something.
「手伝ってくれる？」「無理！今日は忙しいし」
"Can you help me?" "No way! I'm busy today."
そんな高額な買い物は無理だよ。
Buying something that expensive — no way.
7A mathematical sense meaning "irrational." In practice this is almost always seen only within the compound 無理数 (irrational number); it is rarely used on its own in modern Japanese.