No, every odd function is not a one-to-one function.

A function is one-to-one if any two different inputs in the domain correspond to two different outputs in the range.

If and are two different inputs of a function , then is one-to-one if .

Odd function : If a function is an odd function, then . 

Consder a odd function .

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Consder another odd function.

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From equation (1) and (2) and maps the same point .

Thus, every odd function not one-to-one function.

No, every odd function is not a one-to-one function.