In order to understand EDI and develop parsing and persisting for EDI you must fist know about their grammar (Loops, segments and fields). below are EDI Loops for your understanding purpose.
LOOP 1000A PAYER IDENTIFICATION
LOOP 1000B PAYEE IDENTIFICATION
LOOP 2100 CLAIM PAYMENT INFORMATION
As for i know there is no Java API, you must implement their selves. In order to understand their grammar and development guidelines you must purchase their guide (Not open source).
"Health Care Claim Payment/Advice" for ePayment 835
"Health Care Claim: Professional" for eClaim 837