I agree that ' the tea' & 'the oil' does not translate to English smoothly, if we are saying this in English, which we are as a translation, we would say "you drink tea and oil" . As THE isn't present in Turkish, why is it necessary to bring in a non existent word into the sentence when its not required or used for the English version ? The only exception is if you were telling someone they have to drink it as an instruction, and there were other things present to drink as well.
Turkish uses a tricky way to say "the" for direct objects. It's not a separate article, but those tiny little ı on the end of çay (tea) and yağ (oil) mean that they are THE tea (çayı) and THE oil (yağı).
This is technically called the Accusative Case, if you want to read more about it :-)
Also keep in mind that the tiny ı could also appear as i, u, ü because of vowel harmony. And if it comes after a vowel, it will come with a buffer letter -y-.
Ex. kedi (cat) --> kediyi (the cat)
Because the verb is "içersin" (you drink) and not "içerim" (I drink) or "içer" (he/she/it drinks). Similarly, içeriz = we drink; içersiniz = you (plural/formal) drink; içer/içerler = they drink.
More: yerim = I eat; yersin = you eat; yer = he/she/it eats. yeriz = We eat; yersiniz = you (plural/formal) eat; yer/yerler = they eat.
We can tell from the end of the verb. If there is no personal suffix, it means she/he/it (3rd person). The rest of the time, there will be a specific ending to tell us who the subject is:
- içerim = I drink
- içersin(iz) = you drink
- içer = he/she/it drinks
- içeriz = we drink
- içerler = they drink