If you want to delete your stuff on Twitter (and other social media apps) I HIGHLY RECOMMEND the use of the (amazing) app/service known as Redact , which I happen to know someone on the team who built this thing...even if I didn't, I would still recommend it because there's nothing else that I know of like it out there.
Their pricing model for the premium service unfortunately is a bit unbalanced at the moment, due to recent changes that have been forced upon any providers of third party access apps utilizing the APIs of different sites, namely twitter and reddit (who have both increased third party developer access costs for their APIs by an INSANE amount of money, which have to be passed along to consumers somewhere).
That said, you'd be spending literally DAYS AND DAYS if not WEEKS on end trying to manually go through and do all of the deletion and archival stuff you can do automatically in this app, it's really quite powerful and awesome, I won't keep shilling it here, you should go and check it out yourselves. It supports like 30 different social media services/apps, and you can set it up to run on a schedule or to delete certain posts/messages sent looking for a certain word (or lack thereof). You can also back up all of your content to an external spreadsheet and stuff like that.
One of those things I couldn't recommend more highly, especially for those of us here who are security conscious.