I've never done it, but have seen many Chelsea fans doing it... i.e. get on at Imperial Wharf after game. I do go that way both back and forth from work every day and as long as it's working it shifts many people.
The Overground trains are very spacious - one single carriage.
Please remember that:
1) Imperial Wharf doesn't exist as a place, the station is in Sands End Fulham.
2) Clapham Junction doesn't exist as a place, the station is in Battersea (Wandsworth) and not Clapham (Lambeth). Clapham does have a railway station (Clapham High Street) that connects you to...
Ok I'll have a go.
Give yourself 15 mins to walk to Imperial Wharf.
You can jump on anything going south (Overland or Southern) as they all stop at Clapham Junction which is the next stop.
They will be one every 10 mins or so.
You may have to wait for the next. You will fighting for a place...