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

No

While the literal meaning of the word is the same (a casual greeting), the typical usage differs significantly between the two regions. In Brazil, "Oi" is the standard, ubiquitous way to greet almost anyone in informal or semi-formal settings. In Portugal, "Olá" is the standard, natural greeting. While a Portuguese person will perfectly understand "Oi," using it sounds distinctly Brazilian and is much less common in native European Portuguese speech.

Brazilian Portuguese usage:

1. Oi, tudo bem? (Hi, how are you?)
2. Oi, pessoal! (Hi, guys!)
3. Oi, você viu meu celular? (Hi, did you see my cell phone?)
4. Oi, bom dia! (Hi, good morning!)
5. Oi, eu sou o Lucas. (Hi, I am Lucas.)

Portuguese (Continental) usage:

1. Olá, tudo bem? (Hello, how are you?)
2. Olá, malta! (Hello, guys/folks!)
3. Olá, viste o meu telemóvel? (Hello, did you see my mobile phone?)
4. Olá, bom dia! (Hello, good morning!)
5. Olá, eu sou o Lucas. (Hello, I am Lucas.)