(ぐち) To grumble or mutter a complaint, quietly, over and over .
(もんく)   to complain. Often but not always has a childish feeling about it. You’d complain there’s too much fruit in your cake, but you wouldn’t use 文句 about human rights in Somalia.   $$$
クレイム To complain to the management of a store. Usually クレイム is something like, “I bought these socks but there was a centipede inside them! I want a refund!” or “The portions of cheesecake are too small! What happened to the portions?!?”
(くじょう) To complain in a business setting. More polite than クレイム。 For example, if you complain to your friend that your ipod is broken, that’s 文句, but if you go to the ipod store and politely ask them to fix it, that’s 苦情。 If you threaten to sue and call the manager a slag-bag, that’s クレイム。