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

Yes

The spelling, meaning, and grammatical function of "odeio" are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazil, the vowels are generally more open and the rhythm is more syllabic (the "o" is clearly pronounced). In Portugal, the rhythm is more stress-timed, and the unstressed "o" at the beginning of the word is often reduced to a "u" sound, making the word sound more clipped (sounding similar to u-DE-io).

Brazilian Portuguese Examples

1. Eu odeio acordar cedo nos fins de semana. (I hate waking up early on weekends.)
2. Eu odeio quando o trânsito está parado. (I hate when traffic is at a standstill.)
3. Eu odeio comer comida muito apimentada. (I hate eating very spicy food.)
4. Eu odeio esperar o ônibus chegar. (I hate waiting for the bus to arrive.)
5. Eu odeio quando meu celular descarrega rápido. (I hate when my cell phone dies quickly.)

European Portuguese Examples

1. Eu odeio acordar cedo nos fins de semana. (I hate waking up early on weekends.)
2. Eu odeio quando o trânsito está parado. (I hate when traffic is at a standstill.)
3. Eu odeio comer comida muito picante. (I hate eating very spicy food.)
4. Eu odeio esperar o autocarro chegar. (I hate waiting for the bus to arrive.)
5. Eu odeio quando o meu telemóvel fica sem bateria. (I hate when my mobile phone runs out of battery.)