Response I got from Verizon:
The calls you are seeing with 000-000-0086 are for checking your voice
mail messages from this handset. Since April 1, 2004, accessing your
voice mail by dialing your ten-digit wireless number from your wireless
phone will count toward your standard airtime usage and not a free or IN
Network call. Please note: A call to your voice mail box is not an IN
call, as you are not actually calling another Verizon Wireless
customer.
You may still access your voice mail messages airtime free by calling
from a landline phone. To access your voice mail from a landline phone,
please dial your ten-digit wireless number, press "#" to interrupt the
greeting, enter your password, and then follow the voice prompts.
Next, for the 777-000-0001 calls, when using data products and services
such as Get It Now, Mobile Web, Picture and Video Messaging, and
National Access, the phone numbers (777) 000-0001, (000) 000-0000, or (000)
000-0001 will appear in the "Usage detail" section of your statement.
This number signifies airtime that was used by data applications.