Can bolo be used instead of bathao
मुझसे मत बोलो would mean "Don't speak to me"
While बोलना is usually 'speak', it can also be used as 'tell', eg: वह झूठ बोल रहा है (He is telling a lie/He is lying).
'मुझे मत बोलो' as 'Do not tell me' sounds good to me.
why मुझे ? is there an oblique case here?
The Hindi sentence is literally 'Don't tell to me'. मुझे is 'to me'.
Is mujse wrong here?
Mujhse cannot be used with batao. It may be used with bolo though.
Can we also use "mujhko mat batao"?
Yes. 'Mujhko' is just an alternative form of 'mujhe'. Some people see it as being a colloquial form though.
What's the difference between mujhe and mujhse?
You can consider मुझे to be मैं+को and मुझसे to be मैं+से
Generally, मुझे is 'to me' while मुझसे is 'from me' or 'with me'.