Question: What is the relationship between the **EMV** **ODA**, **CA** and issuer certificate during the transaction?

Answer: 
Offline data authentication is the process to verify the cards authenticity.
Terminals are loaded with CA Public key.

* SDA(Static Data Authentication) can assure you the card data has not
been altered after the issuance. SDA card contains Signed Static
Application Data and Issuer Public Key certificate. CA Public key in
the terminal is used to verify the Issuer Public key certificate and issuer Public key is used to verify the signed static application data in
the card.
* DDA(Dynamic Data Authentication) can assure the card data has not
been altered and that the card as a whole is not cloned. DDA Card
Contains ICC Private Key, ICC Public key certificate and Issuer Public Key Certificate. CA Public Key in terminal is used to verify the  

Issuer Public Key certificate. Issuer Public key used to validate the
ICC Public Key certificate. ICC Public key used to verify the dynamic
signature generated by the card using its ICC Private key.
* CDA/AC(Combined Data Authentication with Cryptogram generation) -
Same as DDA card, only difference being Cryptogram Generation
and Dynamic signature happens together assuring that
Cryptogram came from a valid card.
* You should use CA public key to decrypt issuer public key certificate (tag 0x90)
* The decrypted data format is in EMV 4.3 book 2 Retrieval of Issuer Public Key