Polymer 1.0 event handlers don't use the curly brace syntax. Just on-login="onLogin" and all the others as well.
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<firebase-auth id="baseLogin" user="{{user}}" statusKnown="{{statusKnown}}"location="https://himalikiran.firebaseio.com" provider="github" on-login="onLogin"on-error="onLoginError"></firebase-auth><template><paper-menu-button><paper-icon-button icon="social:person" class="dropdown-trigger"></paper-icon-button><paper-menu class="dropdown-content"><paper-item on-tap="login" hidden?="{{!statusKnown || user}}">Login</paper-item><paper-item on-tap="logout" hidden?="{{!statusKnown || !user}}">Logout</paper-item></paper-menu></paper-menu-button></template>
Looks like your firebase element is not in the template, and therefore won't be in this.$
OK, but this.$.baseLogin is missing because the firebase-auth element is not in the template of firebase-login, so it will be undefined. You either have to put the firebase-auth element in the template, or make a direct variable reference to the firebase-auth element for the event handlers.