I am far into intermediate level at this point, but I still have not conclusively found an answer to this. The response that I typically receive is that it's "casual speech," but that doesn't tell me anything about correctness (In English, except for contractions, informal speech is not correct). If you were to ask a university professor of Japanese or a linguist what is grammatically correct, would they say that ending with the plain form of a verb is technically grammatically correct? What about「だ」、「んだ」、and「の」？
Of course a sentence like 鳥は飛ぶ ("Birds fly.") is 100% grammatically correct. It's 100% standard, too; no slang/dialect is concerned. I'm not an expert, but you never need a professor nor a linguist to judge the correctness of such a simple sentence. Don't be that skeptical about your textbook.
But did your textbook really call this casual style? I think textbooks usually call this plain style (as opposed to polite style sentences typically ending with ます/です). This style is used both in formal and casual settings as long as politeness is not necessary. For example, Japanese Wikipedia has literally millions of sentences ending with the plain form of a verb.
Likewise, a sentence ending with だ is 100% grammatically correct. It's one of the most basic word (copula) that corresponds to English "be", after all. It's less common in Wikipedia because である is preferred there, but that's another story. If grammatical correctness is your concern, it's unequivocally correct. The same for のだ.
As for の, are you referring to the explanatory-の used as a question marker? Then of course that's 100% grammatically correct, too. This one is indeed casual and colloquial.