One is simply to make a single attack and damage roll for up to as many adjacent/in melee (grid vs. TotM) opponents as the Fighter's level. Another is to roll a die with as many sides as the character has levels, and have them kill that many foes within reach, abstracting out that average damage is going to equate to average HP for 1HD foes, and subsuming the attack rolls in that single die. So for a 4th level fighter, they can simply kill d4 Orcs per round. For a 5th level Fighter, you can simply roll a d6 and re-roll 6s. Same with a 7th level fighter and a D8.
Joshua Macy, on his blog, alternately suggests rolling a number of d6s equal to the number of attacks allowed, with a target number from 3-6 based on what kind of armor/AC the opponents have. He made a nice table converting the numbers needed to hit given ACs on a d20 to d6s with a little rounding. This lets you factor in the armor class but still get the attacks resolved quickly with a small handful of dice.