Taṇhā: Craving
Taṇhā is thirst, the mind reaching for whatever it wants. That reaching is what stirs when the flesh "lusteth," and it starts moving before you have agreed to it. It leans toward the next taste or comfort the way a thirsty person leans toward water, and that leaning is the pull that sets the flesh against the Spirit. Nothing dramatic is needed for the war to begin; the quiet tug toward more is already the first shot.
Kilesa: Defilements
Kilesa is the grime on the mind. "The flesh" is the whole grimy side of a person, always tugging toward the easy thing while a clearer part wants the good. Clean water and muddy water cannot fill one glass at the same moment, so the two keep swapping places, and that endless changing of seats is why they stand "contrary the one to the other."
Anusaya: Underlying tendencies
Anusaya is a habit lying asleep in you, out of sight until something stirs it. This is how the flesh can "lust" the instant after you firmly meant it not to: your wish sat on the surface while the old craving waited underneath. Like a coal buried in ash it looks dead, then a small draft brings back the flame, and the resolve you made a minute ago is overrun.
Anattā: Not-self
Anattā means no fixed self sits inside you owning the body and handing down orders. "Ye cannot do the things that ye would" is the plain evidence: were a master at the controls, it would tell the flesh to obey and the matter would end. Tell your own craving to stop and notice how little it heeds you, the way a rider learns the horse was never his to steer. The failure of will you feel is not weakness in the driver; there is simply no single driver there at all.
Padhāna: Right striving
Padhāna is the steady effort to starve the low pull and feed the higher one. This is "the Spirit against the flesh" taken up as daily work: catch a craving while it is small, set it down, and lean the other way. Like pulling weeds it is never finished in one morning, yet each pull keeps the whole garden from being lost.