Is it safe to mix hydrocodone, ibuprofen, and naproxen or aspirin?

Not recommended. This would not be recommended as it would increase the risk of gastrointestinal bleeding.
Yes. Ibuprofen is a non steroidal anti-inflammatory medication. Hydrocodone is a narcotic. You can take them together. However, it is not recommended to take Ibuprofen, Naproxen and Aspirin together.