By straps, do you mean the drawstring at the end? The rain sleeves I have are fairly simple long plastic tubes, that can fit the camera body and long lenses, with a downsloping hand access where you can insert your hand in from the bottom to get at the camera controls. There's a hole for an eyepiece where you can alternately remove the eyecup, slide the eyehole around your viewfinder, and then reinsert the eyecup to allow shooting through the viewfinder. At the lens' end, there is a drawstring, which can be pulled tight around your lens hood, allowing you to keep shooting in rain as long as you just keep the camera pointed horizontal or downwards...if the weather gets really ugly, you can pullthe sleeve past the lens' opening, and pull the drawstring closed all the way.
I wouldn't trust this type of thing to keep the camera dry while shooting surfers in Hawaii from inside the wave, or going down a rapids in a raft...but for even heavy rainshowers or splashes/spray, it works fine for me and is quite cheap.
EDIT: Now I think I understand what you're saying - how does your camera strap work with this product!! Sorry for the misunderstanding - actually it works pretty easily for me - because you have the hand insert section at the back and bottom, the strap simply lies down into that section. If you have a long neck strap, it would stretch all the way out of the hand access hole - or you can do as I do, and wrap the neck strap twice around your wrist as you insert your hand into the hole - your hand stays inside the hole to shoot, and the necks trap stays inside the plastic cover wrapped around your wrist.