Load only one translations file.

functions.php

<?php
function theme_name_setup(){

	$domain = 'theme-name';

	if ( $loaded = load_theme_textdomain( $domain, trailingslashit( WP_LANG_DIR ) . $domain ) ) {
		return $loaded;
	} elseif ( $loaded = load_theme_textdomain( $domain, get_stylesheet_directory() . '/languages' ) {
		return $loaded;
	} else {
		load_theme_textdomain( $domain, get_template_directory() . '/languages' );
	}

}
add_action( 'after_setup_theme', 'theme_name_setup' );

plugin-name.php

<?php
function plugin_name_load_plugin_textdomain() {

	$domain = 'plugin-name';
	$locale = apply_filters( 'plugin_locale', get_locale(), $domain );

	if ( $loaded = load_textdomain( $domain, trailingslashit( WP_LANG_DIR ) . $domain . '/' . $domain . '-' . $locale . '.mo' ) ) {
		return $loaded;
	} else {
		load_plugin_textdomain( $domain, FALSE, basename( dirname( __FILE__ ) ) . '/languages/' );
	}

}
add_action( 'init', 'plugin_name_load_plugin_textdomain' );