The cheapest way I've found to Elstree, although you have to like walking and have a bit of time, is:
Jubilee line to Stanmore.
Walk to Canons Corner (about 10-15 mins)
Bus to Elstree village - sorry, forget which one, but if you turn right out of Stanmore station and then left at the roundabout, it stops at the bus stop there (Approx. 10 min journey, bus frequency is about 20-30 mins)
Walk to airfield (a further half hour odd)
As I said, you have to have a fair bit of time!