To use Straight Talk on CDMA providers Verizon or Sprint, you have to buy the Straight Talk-branded phones that have been approved by those carriers. There are no "unlocked" CDMA phones on Straight Talk for the CDMA signal carriers. The phones to connect to the two CDMA networks with which Straight Talk are locked to a specific carrier (Sprint or Verizon), and you can only use the phones Straight Talk sells.
For Straight Talk "Verizon" specifically you have look carefully at the phone's product code to determine if it is going to run on Sprint or Verizon. Many Straight Talk people have been disappointed as the the better of the obsolete Androids run on ST "Sprint", not ST "Verizon".
The Straight Talk "Verizon" iPhone 5 is CDMA + GSM. On that phone, the GSM port its unlocked (so people buy it and stick in a ST "AT&T" SIM card) even though the CDMA part its locked on Verizon.
With the exception of that dual purpose iPhone 5, all other Straight Talk-branded phones are from previous generations, 2 -5 years old. Typical MNVO lineup.
This is why the Straight Talk & Net10 BYOP SIM card plan was so revolutionary. Bring the HSPA phone you want, the specs you want, and run it on AT&T or T-Mobile (depending on the sim you choose). The parent carrier doesn't have to approve it first.
Lots of people are running Galaxy SIII, Galaxy Notes, Galaxy Nexus (me), LG Nexus 4 on Straight Talk/Net10 using the BYOP sims.
Straight Talk sells phones that work on AT&T, Verizon, Sprint. They also sell (or sold) sim cards for Bring Your Own Phone (BYOP) for AT&T and T-mobile. The ST "AT&T" sim cards have disappeared from the Straight Talk website, but you can still find some at local Wal-marts and eBay (at much higher prices). You can also still buy "AT&T" and "T-mobile" sim cards from sister company Net10. There's been MUCH discussion about the sim card situation, and lots of secrecy from the companies involved.
Also, there is a specific subforum dedicated to Straight Talk. You may find more answers there than in the "general" section.
US Prepaid/MVNO Discussion > Straight Talk
Sent from my Samsung Galaxy Nexus (GT-i9250).