There are no Tube lines running into Waterloo from your direction. There's only the same National Rail line that you'd be using if you caught a train from either Basingstoke or Newbury. So it's stations along that route that you'd need to investigate if you wanted to drive part of the way.
The walk from Waterloo to the Strand isn't too bad for someone who's fit and able but, if you'd rather take a bus, route 26 can get you there. As you arrive on the concourse at Waterloo (i.e. with the trains behind you), turn right and walk to the far end. There are stairs and escalators down to the street there, with the stop for route 26 being very close to the foot of them.