Hello hummingbird-43,
Messages that you receive from blocked phone numbers would need to be deleted manually. Delete messages on iPhone has those steps for you.
"Delete a conversation
- In the Messages list, swipe left on the conversation, then tap
.
Note: Deleted messages remain in your Recently Deleted folder for up to 30 days, and you can recoverthem. To permanently remove a message, tap Edit (or Filters) in the top-left corner, tap Show Recently Deleted (or Recently Deleted), select the messages or conversations you want to remove, tap Delete, then follow the onscreen instructions."
You also mentioned deleting blocked contacts and numbers. We want to make sure you're aware that completing these steps would essentially "unblock" this contact information, meaning they would have the ability to call, email, or message you again. Find those steps in Block phone numbers, contacts, and emails on your iPhone or iPad.
"Manage your blocked phone numbers, contacts, and emails
To see the phone numbers, contacts, and email addresses that you've blocked from Phone, FaceTime, Messages, or Mail:
Phone
Go to Settings > Phone and tap Blocked Contacts to see the list.
FaceTime
Go to Settings > FaceTime. Under Calls, tap Blocked Contacts.
Messages
Go to Settings > Messages. Under SMS/MMS, tap Blocked Contacts.
Mail
Go to Settings > Mail. Under Threading, tap Blocked."
If you're wanting to delete the contact information from the contacts app, this is done manually using the steps in Manage and delete contacts on your iPhone or iPad.
Cheers!