SCT Controller reported conflicting information between facility status board; published NOTAM; ASOS; and pilot information at LGB airport. Controller reported this conflicting information could lead to pilot use; or controller assignment of an unusable runway.

Narrative

I was working Coast area mid configuration. Before the event my coworker briefed me that the night crew had put incorrect information in our status board and that LGB ILS was in fact in service. Fast forward to XA:45. Aircraft X called me on the phone for a clearance and a release off LGB airport stating they would depart runway 26R. Our board said Normal closures for LGB meaning 26L/R closed and Rwy 30 open. I told the pilot that I was showing 26R closed and 30 open. They said the ASOS says 30 closed. I looked up the printed NOTAMS and said 30 will closed on Day 6 and its Day 0. Same for the ILS; although not relevant to this departure. I then stepped away from the sector to check a computer for up to date information and said the same thing 30 closed Day 6. Pilot said 26R looks open but so does 30. Pilot listened to ASOS again and said Rwy 30 in use but also Rwy 30 closed. After the pilot taxied to both runways and we talked about it we determined that Rwy 30 was safe to depart and departed rwy 30. I was left very uneasy about the whole situation. The night crew per SOP is supposed to update our board and check NOTAMS. The 26R/L closure is a daily closure from 0600-1500z so its not NOTAMed. How does the airport mark or tell pilots about this closure? We need a better system here. What happens if someone uses that runway? Recommendation: Our NOTAM system is hard to interpret and we often make mistakes. I know our staffing isn't great right now but if we could have these conversations with our coworkers and leadership actually got involved we could all figure out ways to minimize these events.