On East Coast at the moment, in normal operation:
the mark 4 DVT has space for seven bikes on something a bit like "sheffield stands"- ie level. They have confirmed that they can accomodate, with a little notice, tandems and some other non-standard cycles. From memory bike reservations are given as "coach P"
The HSTs carry bikes in the guards van part of the TGS. This takes three bikes, hanging by the front wheel, no non-standard cycles. Given as Coach A for reservations.
The Scotrail HSTs will take bikes for intermediate stations in a converted loo, that will be too small to cope with, for example, standard mountain bike handlebars (now typically 700mm wide) without issues. They've also sad they'll take end-to-end reservations in the power cars.