FAO Mairi
The 'sticky out' bits you refer to on the wing are the boat or canoe fairings.They provide an aerodynamic covering for the trailing edge flap drive system.The Number 3 and 6 fairings behind the engines are shaped differently from the others.The inboard flap section runs from the fuselage body fairing into these (The flap outboard of the engines is a totally different section).There is a channel cut out of the inboard face of the engine pylon boat fairing at production which allows the flap mechanism to run back along its track(which is hidden by the fairing).When the flaps are up this hole is filled by a spring loaded plate,referred to by Boeing as the 'Inboard Flap Midflap Torque Shaft Clearance Door'.
The CDL -an approved document that shows the crews and us engineers what panels/doors/components the a/c can fly without -allows the 737-300 to fly minus both these doors (one on each wing) with only a minimal enroute climb fuel penalty.Perfectly legal and perfectly safe.
We use this gap to access the flaps for part of their lubrication procedure but,trust me,it's not a panel you can manually open or leave 'undone'.The spring is very strong and the door is only opened and closed by extending/retracting the flaps.
Hope this helps!