I am looking to create a language that has no more than 20 words. What 20 words can I use that, when combined with each other, can be used to say basic things.
a word for small + a word for person = child
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According to Wikipedia's article on Semantic Primes, you'd need about 60 to say everything. Is that too many?
Since "small person" doesn't mean "child", this indicates that you're willing to put up with phrasal idioms, like "kick the bucket", where the meaning of the phrase has to be learned separate from the meaning of the individual words. In that case, it does not matter what the meaning of the 20 words is. The words can therefore be ta, ti, te, to, tu and so on. The word "pu" uniquely means "end of phrasal idiom". Then, "ta pi ko pu" is an idiomatic phrase meaning "cow", "pi pi su pu" is an idiomatic phrase meaning "grass", and so on.
If you want to impose a requirement of strict semantic compositionality at the phrasal level (a draconian requirement not obeyed by any actual language), then you wouldn't be describing a human language, since human languages don't have vocabularies of only 20 words. I don't know how the concept of "expressiveness" could apply at all to such a system. There's no metric of expressiveness, anyhow, other than "unbounded; infinite".