His speech today was full of exaggerated words, and I couldn't really tell what he was trying to say.
Literal
Today [attributive-の] his speech [topic-は] excessively exaggerated [attributive-な] words [subject-が] many-[te-reason-くて] what [object-を] is-saying [question-のか] well was-not-understood.
やたら ('excessively, absurdly, way too much') is a colloquial intensifier expressing mild exasperation. 大げさ ('exaggerated, over-the-top, grandiose') is a common na-adjective. 演説 ('speech, oration') is formal — the kind of speech politicians, CEOs, or ceremonial figures give. ~のかよくわからない 'I don't really know (the question of) what X' — using のか to embed a wh-question.