What a great question! I think that there is more than one answer, but a few likely theories come to mind. Aside from just a stylistic choice (meaning that Junot Diaz maybe just liked the sound of the Spanish words mixed in with English, and that is the sole reason he put them there) on the part of the author, the untranslated Spanish words in an English text can serve several different purposes.
An untranslated word, especially a repeated one, in an English text read by a non-Spanish-literate reader creates some Spanish learning over the course of the book. Either the English reader can't take the suspense anymore and looks the Spanish word up in a dictionary (or asks a Spanish-speaking friend to translate) or, which is more likely, the English reader learns the Spanish word from context. This means that the situations described and the words around the Spanish word help the reader figure out what the Spanish word means. Things learned from context (which is almost entirely how babies learn language, although in that case it's auditory context) are well-remembered: when it's hard to learn something, and it takes you a while to figure it out, often that learning stays with you. So Diaz, a bilingual American, is pulling the English reader into his Spanish/English-speaking world. He's making the English reader read Spanish -- as some of the characters in the book who are a Spanish readers/speakers have had to read English.
The untranslated words also add an air of mystery that makes the story interesting. If you don't know exactly what the word is that people are talking about (like puta for example) they might keep reading in part to figure out what is being talked about! Diaz has just enough untranslated words so that the story doesn't become obscure. You can still follow the story without translating the words -- but maybe you read further just because you want to find out what the word means!
Certain words truly are untranslatable; fuku, for example, isn't easily explained in Spanish or English. Learning what it means from context is perhaps the only way to get an approximation of what fuku means for a person who is not part ofthat culture. Diaz does explain what it means at the beginning of the book (one of the few words he actually does that for), but the full meaning of the word and its significance in the story are really only revealed as the story goes on, with characters using the word repeatedly.
Certainly there is something of the alienation that the immigrants from the Dominican Republic felt when they came to the US imparted to the reader by the use of Spanish words. Everything in the US was in English for those immigrants-- every word had to be learned and remembered. For the reader to experience some of this, by reading untranslated Spanish words, is to feel a small part of this alienation and confusion.
Diaz makes a lot of unorthodox choices in this book (such as the non-linear storytelling, and the extensive use of entertaining footnotes!) and the use of the Spanish words is one of them. Think about what you thought and felt reading them -- if you are a Spanish speaker/reader you may have thought something very different than if you are not. Explore your reactions to the words and include them in your answer.