Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
First let me explain a few things. Each application you downloaded using a particular Apple ID is tied to that ID/email address. That means whenever you try to update those apps from App Store, it will still ask for the old Apple ID/email regardless of what ID you signed on your iPhone now. So what you want to do is, just delete those application that needed update and redownload them using your new or non-disabled ID/email.
Also, Apple usually disables the App Store part of ID if they notice any issues with payment method on your account, like invalid card, refunds etc. You will still be able to sign in and make changes to the account, but you will not be able to use App Store and iTunes Store part.
Go to Settings > iTunes & App Store. Then tap the ID and tap Sign out. Then sign in to a working ID.
Remember, you have to create a brand new Apple ID (not change the ID of old one) and then sign in to it on iPhone. Then delete those apps and download a fresh version from App Store.
You can create a new Apple ID from here if you have not already done (you have to use a different email to create new ID) --> https://appleid.apple.com/account
Please let me know if that didn't work, so I will continue to help you