How to call vuejs function from javascript function?

Would be easier if the code you posted would be complete but my guess is:

Use arrow functions

var successCallback = payment_id => {
    // now "this" refers to this vue component instance so:
    this.order()
}

or store reference to this and use it like a variable

var that = this
var successCallback = function (payment_id) {
    // this is *this* function
    // "that" is a vue instance
    that.order()
}