This is pretty much my old commute so here goes:
Two one of two options to get to a point between Southall and Hayes..
a) Take the Thames path to Kew Bridge, cross over to the North side of the River and take the road running alongside the river until you get into Brentford. Then onto the grand union and keep pedalling 'till you get to the junction with the Paddington Arm of the canal.
b) Somewhere around little venice, Get on the Paddington arm of the grand union and head west 'till you join the main stretch of the canal.
From here the most direct route for Terminals 1,2 & 3 is probably to take cycle path from the Hayes by pass to the Bath Road, then along the Bath road until you get the chance to get onto the perimeter road. For T4 get to the Bath Road as above but carry on along the Parkway until you reach Hatton Cross then follow the perimeter around to T4. T5 is probably easier to carry on the canal to west Drayton, couple of back roads will take you to 'wise lane' where you can pick up an off road route through some park/common land until you get to Longford where you can pick up the Bath Road heading East to the terminal building.
The canal does appear to go a long way round but it is actually pretty quick when compared to the local cycle paths which have to cross a lot of junctions and are very stop/start. Of course if you're just in a hurry then get on the A4.
If it were me I'd go the Thames / Brentford route. Bit better surfaced and a little more interesting.