SA CIVIL AVIATION REGULATIONS
PART 91: GENERAL AVIATION AND OPERATING FLIGHT RULES
91.03.4 Air traffic service flight plan and associated procedures

(4) The ATS flight plan shall be filed in respect of

(a) all flights to be conducted in controlled or advisory airspace: Provided that this requirement shall not apply in respect of

(i) a local flight;
(ii) a flight crossing an airway or advisory routes at right angles; or
(iii) a VFR flight entering or departing from an aerodrome traffic zone or control zone, from or to an unmanned aerodrome and where no other controlled or advisory airspace will be entered during the flight;

Let's examine the given options:

Must file a full IFR flight plan to cross any airway. → INCORRECT. Aircraft flying under VFR can enter controlled airspace (including airways) with ATC clearance.

May cross the airway at any time without communicating with ATC. → INCORRECT. Controlled airspace always requires communication and clearance.

Must climb to at least 10 000 ft before crossing the airway. → INCORRECT. Crossing altitude depends on ATC clearance and airspace structure.

May fly through the airway without filing a flight plan provided clearance to do so is obtained from the ATSU responsible for that airway. → CORRECT. An airway is controlled airspace, typically used by IFR traffic. Even if you’re on a VFR flight in mostly uncontrolled airspace, once you intend to enter or cross controlled airspace, you must establish communication with ATC and obtain the necessary clearance. However, you do not need to file an IFR flight plan just to cross it.