Midterms start next week. Cramming the night before won't cut it — these problems are impossible to handle that way. Start today.

Literal

Next-week from mid-test is. Night-pickle [using-じゃ], handle-can-not [attributive-の] problems only-[emphasis-ぞ]. Today from begin-[imperative-ろ] [emphasis-よ].

A rich multi-sentence passage. 一夜漬け ('one-night pickling') is a metaphorical idiom from food preservation — 'cramming the night before' (like pickling something overnight). 太刀打ちできない ('can't fight / stand a chance against,' literally 'can't wield a sword') is a set idiom. ~ばかりだ ('only / nothing but') intensifies. Plain imperative 始めろ directly orders.