Cleanup Duplicate Contacts (for iOS) and Go Contacts Pro (for Android) start the task right by helping you merge or delete redundant listings in your contacts file—like those six entries for your college roommate.
My Contacts Backup (for iOS) and People (for Android) let you save your contacts in a vCard format, allowing you to move them all to cloud storage, using the depository of your choice: Apple, Gmail, Outlook.com, etc. You should then email that .vcf file to yourself, so you can edit it further on a computer, then sync your “squeaky clean” new contacts list with your phone.
Contact Remover (for Android) and Spring Cleaning (for iOS) take care of the last step: deleting from your phone all those old, messy contacts entries. Like the other apps in this list, neither costs more than $1.