Learn Croatian: Ne mogu kuhati jer nema ulja. - I cannot cook because there is no oil.

The base word for oil is ulje. However, after the word nema (meaning there is no), Croatian requires the following noun to be in the genitive case. For neuter nouns like ulje, the genitive ending is -a, making it ulja.

Does nema mean 'there is no' or 'he does not have'?

It can mean both! Nema is the negative form of ima (he/she/it has). But just like ima is used to say 'there is', nema is used to say 'there is no' or 'there isn't any'. When used to mean 'there is no', it always forces the next word into the genitive case.

Why is kuhati in its dictionary form (infinitive)?

Because it comes after the modal verb mogu (I can). When you say you can or cannot do something in Croatian, the main action word stays in the infinitive form, very similar to how it works in English.

How do we know who cannot cook if the word ja (I) isn't in the sentence?

The verb form mogu is specifically the 'I' form of the verb moći (to be able to). Since the verb itself already tells us who is doing the action, the pronoun ja is usually dropped unless you want to add special emphasis.