Is the word oito the same in Brazilian and European Portuguese?

Yes.

The spelling, meaning, and grammar of "oito" are identical in both Brazilian and Continental Portuguese. The only difference is the pronunciation. In Brazil, the vowels are generally more open and the final "o" is pronounced clearly as a "u" sound ([ˈojtu]). In Portugal, the pronunciation is more clipped and "swallowed," with the vowels being more reduced and the rhythm being more stress-timed.

Brazilian Portuguese Examples

1. Eu tenho oito anos. (I am eight years old.)
2. São oito horas da manhã. (It is eight in the morning.)
3. Comprei oito bananas no mercado. (I bought eight bananas at the market.)
4. Ele chegou às oito horas. (He arrived at eight o'clock.)
5. Tem oito pessoas na sala. (There are eight people in the room.)

Continental Portuguese Examples

1. Eu tenho oito anos. (I am eight years old.)
2. São oito horas da manhã. (It is eight in the morning.)
3. Comprei oito bananas no supermercado. (I bought eight bananas at the supermarket.)
4. Ele chegou às oito horas. (He arrived at eight o'clock.)
5. Há oito pessoas na sala. (There are eight people in the room.)