My new deck will be 16 ft. wide by 24 ft. long. Will it be okay to run the boards lengthwise (the 24 ft. length)? My joists are running the 16 ft. length. I just want to know if this will look okay. having difficulty visualizing it.
Yep, you can run the boards either way. However, running the boards parallel or with the joists means you need to install blocking on 16-inch centers (or less), to match the joist spacing. It should look like a waffle. Deck boards are quite thin and NEED equal and frequent support.
2x4's might be fine for any person's "load", but I'd go with a minimum of 2x6's as this will help to stiffen the entire deck's structure. Otherwise, it'll look like a pier or dock (purposely perpendicular to the length) and you should be seamless or installing singular 16-foot boards for the best look.