When on the admin view you can use the following functions to get update data.
If you want to build your own functions, then you can get update related data from site transients update_themes, update_plugins, and update_core. Then you can compare the plugin and theme transients with the theme and plugin arrays you can get with wp_get_themes() and get_plugins(). The above functions are more or less wrappers for these transients and functions.
Have a look at the source for the functions to see how WP handles this stuff.