The WP Category Sort plugin allows you to easily reorder your categories the way you want via drag and drop.
- Upload the wp-category-sort.zip file Via WordPress Admin > Plugins > Add New,
- Alternately, upload wp-category-sort folder to the /wp-content/plugins/ directory via FTP,
- Activate the wp-category-sort plugin from Admin > Plugins.
Does this plugin require me to overwrite WordPress core files?
No, there is nothing more you have to do except uploading and activating the plugin.
Does this plugin allow me to reorder subcategories as well?
Yes it does.
Awesome, It does what I exactly want. Thank you!