I take hydrocodone 5-325 daily for chronic neck pain and migraines. How many per day can I take before it will hurt my organs?

Difficult to say. In general opioids are very safe long term. Perhaps even more dangerous is the tylenol (acetaminophen) often associated with the opioids - in your case the 325mg. Please be sure to keep total daily dosage under 4000mg, long term i would suggest less than 2000mg. Finally have your doc check liver and kidney function every 6months while on these meds.
2000mg per day. You really need to seek out a spine /pain specialist in your area to find the actual source of your pain and treat that rather than covering it up with narcotic meds. But, to answer your question, the only real organ issue would be the liver. It's not recommended to consume more than 2000mg of Acetaminophen (the 325 in each norco) on a regular basis. Even less if you consume moderate alcohol.