You can easily cut down on the amount of Spam messages you receive on Twitter by following these steps. Unfortunately there really nothing you can do about people creating fake / sock puppet accounts to send you harassing messages, besides blocking those individual accounts. Here's how to stop receiving direct message from people you don't know using the iOS app:
1. Open the Twitter app on your iPad or iPhone.
2. Click the "Me" icon in the lower-right hand corner.
3. Click the Gear icon.
4. Click "Settings" from the pop up box.
5. Under Accounts tap the account you want to make private.
6. Under Privacy tap the "Receive Direct Messages from anyone" slider so it is OFF/WHITE.