"Gender" refers to languages that have 'masculine' and 'feminine' forms of words. For example, in Greek 'masculine' words usually in in -os, -as, -es, etc., while feminine words usually end in -a, -e, etc. Natural gender refers to things that actually male or female, like "man," "woman," etc. Linguistic gender has to do with masculine vs. feminine word forms, and may describe words that are neither 'male' or 'female.' In Greek, for example, the word for 'river' is 'potamos.' Because it ends in a masculine ending, the word is considered linguistically masculine. In reality, however, rivers are neither male nor female.
Grammatical gender is a system in grammar, in which nouns are classified as belonging to a certain gender - often masculine, feminine, nouns with natural gender, such as "boy" or "girl," must agree in grammatical gender with any pronouns used to represent them. Therefore, "She is a nice boy" is ungrammatical.