In reply to Sharp:
you need to define strength here.
legionnaires etc dont really gain absolute strength during stressed phases, but they do gain efficiency due to upping their oxygen intake and as their weight drops their strength to weight ratio improves (to a degree, obviously it then plummets again). a lot of 'strength' is recruitment and efficiency. depending on the phase, they sometimes go into stressed phases on the back of strength and recuperation ones.
the classic legionnaire stuff is also on the back of minimal sleep, which is when muscle does much of its growing, reducing the mass the body can simply gain.
they are not gaining the same sort of strength as powerlifters and to an extent bodybuilders (who control their sleep as much as their diet), and who also have heavily periodized regimes (gaining, cutting, bulking etc).
if you want to gain strength as a priority (over body composition) then train, rest, recover and eat well at the carb/protein ratios best suited to whatever strength style your after. spend optimal time pulling/lifting around your 1RM.
if you want the legionnaire look, stick around your 5RM, add lots of cardio and 20RM stuff, eat just above your required intake and dont sleep too much.