Re: My samsung galaxy core is stuck in Odin mode
Can you turn it off at all? Maybe by renoving the battery (I do not know if it is removable in that model)? Maybe then when turning it back on it will boot into the Android system.
I imagine that Odin mode is the download mode, right? Then you might be able to re-flash the stock ROM via Odin, if nothing else works. You can search for your stock ROM at the Sammobile site.