Learn Italian: Ho diciannove o venti euro. - I have nineteen or twenty euros.

For numbers 17 to 19, Italian puts the 'ten' part first, combining dieci (10) and the single digit. When dieci and nove (9) smash together, the consonant doubles to make pronunciation smoother, creating diciannove.

Why does venti (20) end in '-i'? Does its ending change depending on what I am counting?

No, it doesn't change! Numbers (except for one, uno) do not change their endings to match nouns. While '-i' is usually a plural ending for nouns, for the number twenty, venti is just how the word is always spelled.

Since I have more than one, why is the word euro not pluralized to 'euri'?

In Italian, many foreign loan words and short currencies do not change their endings in the plural. You say un euro for one, and venti euro for twenty. The word stays exactly the same.

There is an ho and an o in this sentence. How do I pronounce them?

They are pronounced exactly the same, sounding just like the vowel sound in the English word 'or' (without the 'r')! The letter h is always silent in Italian. It is only added in writing to help you tell apart ho (I have) from the word o (or).