You could try units of 5 with 1 attack with 4 effective aid anothers, simulating lots of spears/arrows etc. but I agree with two of the posters above. Either just narrow down the combat to a small scale combat and that represents the pivot point of the larger combat or set up a Victory point set of conditions for hitting certain objectives.
Both would work well.
HOWEVER it would be COOL as BALLS! to hack through 50 elite style orcs.
I was once part of such a mass combat and still remember it years later.
Move them in groups of 4. One attack, 3 aid anothers (assuming all can get position). Killing one weakens the unit. Single or dual orcs retreat/withdraw and form a new unit which attacks again... creating an interesting wave dynamic. Make the orcs 20 hps each. Round damage to the nearest 5. Play smart(ish) if its getting so they are too clumped up? Have them withdraw and then try a flanking proposition. Each unit of 4 should be 20ft from the next unit of 4 until they can actually close. This is good against fireballs, artillery etc. Orcs ARE trained to war.
I'd also include a few ogres as shock troops as well and maybe some sort of cavalry style troops.
Your party is 10th level? Then sorry, level 3 orcs are not going to be much of a speed hump even in the numbers proposed. Your wizard should be able to take out 8-12 minimum with one spell.
I recommend an initial wave of skirmishers. Call it about 50 level 1 orcs - use them in units of 10. They'll soak up a fireball and some area affect spells, Get the fighters excited etc
Then send in your first wave of level 3 orcs. Call it about 30 of them. Send in some cavalry as well. Throw in a leader. Have them move in a staggered ragged wave - area effect spells will work but not so much.
Then your final wave. 30 more level 3 orcs with ogres and a level 6 leader or two. Maybe some minor spell casting support like a shaman buffing them with bless etc.
Most importantly? Tell the players to prepare for an all day combat session and set aside 5-6 hours.