House Or Rental
Here is a VRBO site that may be of help. Be careful of extra fees on some of them. Southport is also very close to Oak Island & may be worth the lower price if you want to be close but not pay the fees for the Oak Island location.
House Or Rental
I think these are a little pricier, but wanted to list it as an option. You can play with the number of guests based on if you're going to share with a larger group, or want something smaller.
Hotel
I just dropped in Expedia on here, but feel free to use your own favorite search engine. Southport is very close too & several guests have booked rooms there!