In a 501c are we allowed to invite the public for the purpose of fund raising ie; lunches,open houses, barb-q

In general, yes. What aspect of inviting the public to your fundraisers do you think might be a problem?

To properly answer this we need to know what type of 501(c) is it - it makes a difference whether this is a charity 501(c)(3), or a social club like a 501(c)(7). Also if the amount of fund raising from sales (such as a BBQ) exceeds "safe harbor" rules there can be sales tax and federal tax implications.