Question

Electric flux through a closed surface is zero due to charges outside the surface ?

Answer 1

You can think of the flux as the number of field lines passing through a surface.

For the situation that you are thinking of, consider a positive charge located somewhere outside of a spherical surface. The electric field lines will be radiating outwards from the positive charge. Now, on that portion of the surface of the sphere which is closest to the positive charge the field lines will intersect the surface going "inwards" across the surface of the sphere and they will therefore contribute a negative flux. However, these same field lines must also exit the sphere going "outwards" on the side of the sphere furthest away from the charge. Here they contribute a positive flux. The sum of the negative and positive fluxes is zero.

Another way to think about this is, since there are no charges within the sphere (by assumption), all of the electric field lines from the positive charge that enter the sphere must also exit the sphere. Therefore there are as many field lines contributing negative and positive flux.