Yes, both are almost the same. But to choose the good one, "eu odeio" comes from "ódio" substantive, which means "hate", the oposite of "love".
For sure "Odeio" is stronger and a bit more emotional, let's say...
Eu odeio Justin Bieber - I hate Justin Bieber (if possible you would insult him, because you hate him)
Eu detesto Justin Bieber - I deslike him a lot (maybe you deslike him a lot, but maybe because his songs are not that cool. But you can deal with haha)
In case of doubt, just go foward... the difference is not that far, because at least Brazilians are emotive speakers... we say we love and hate things all the time...
is this clear? let me know if not :)
Bons estudos!