I've never had luck with unsubscribe tools.
The best practice for any email inbox is to start organizing early and be careful about what gets directed there. Since that's long past, I would (and have for a few addresses - mostly family members') start slowly unsubscribing from each of the sites you're getting email from, one-by-one. After I've unsubscribed from each service, I'll do a mass-search for all emails from that site and then delete them all. It's an easy way to keep track of what you've deleted.
The process takes time, but you can know that each site is being removed. Some take a try or two and sometimes you'll get emails from sites that sell your data - the key is not to get frustrated.
As you're doing this, start building an organization system with folders/labels. Setting up auto-sorting rules is really helpful, too. Soon, much of your inbox will auto-sort itself by category and you'll be able to focus on what's important while quickly removing junk.
Perhaps others will have insight into using third party tools, but like I said I've never had luck with them.