My mother told me so is the most natural in this context. My mother told so to me - not natural, sounds stilted. Co my mother told me.
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Mister MicawberIn the context you have provided, none of those would be used.Teacher: English is very essential because it is an international language.Me: Yes, I agree with you. My mother told me that, too.In a different structure:Teacher: Why do you think English is an international language?Me: Because my mother told me so. / Well, so my mother told me.
Mister MicawberTo me, 'someone told me so' is an answer to a question or an explanation for the speaker's own asserion.