As a reverse POV - how many modern day soldiers will freak out when you have your enemy at arms reach row upon row, you can't get any more close and personal. Do modern day soldier have guts to endure Legionaires day job?
On the topic of food: The Marines food supplies should if rationed properly be able to sustain them for a period until they acclimatize to the local livestock and water. Also, I would think that cooking food and using their water purification units would help with preventing illness.
On disease: The many vaccinations that the Marines receive should protect them against a relatively broad spectrum of illnesses, and if the Marines can keep the wider Roman populace at a distance, then there should be little exposure to many disease vectors. The greatest threat to the marines will be insect, rodent and food-borne diseases. Cooking will kill many food diseases, insect repellent (in clothes and as a topical lotion) will protect quite effectively against ancient insects and establishment of a good base should keep rats to a minimum.
The war that this MEU I would assume would be rather like Afghanistan, Iraq or Vietnam where the units are no longer mobile strike forces. This would conserve fuel, prevent wear and tear, and allow creation of good static defensive locations. The Romans would not immediately attack such an alien force (They would be smart just to observe), and the Marines can zoom around and pillage the surrounding countryside for resources whilst creating their base, perhaps in a village.
Marine attack aircraft and Scout snipers would decapitate Roman leadership. Sure, the plot of this fantasy story is that all attack aircraft are destroyed and only transport craft left, but I'm pretty sure that the UH-1 and the AH-1 have significant parts commonality. Also, mechanics are innovative people. They can figure out how to recycle parts of the destroyed attack craft.
But since the story allows for "transport aircraft" does that mean we can use the Hercules? Because holy cow that thing would make for a nice bomber. Also, I think the Sea Stallion could be flown purely as a psychological weapon. Pop off a few flares as well, and drop a leaflet or two over Rome informing them of their new Marine Gods...
When actually fighting the Romans, the best strategy of the Marines would be to avoid close combat and to use the advantage their stand-off weapons afford them, and try to attack very large roman formations at a significant distance. I think a 155mm round from a howitzer would nicely counter the best siege weapons of the Romans, and would easily tear through large concentrations of Roman troops.
Thinking of artillery... a HIMARS rocket system with those exploding submunitions would make for an incredible weapon...
Now after the Marine snipers and attack craft have killed the leadership, the shock and awe of artillery and the psychological impact of aircraft have killed, maimed and terrified many of the Romans, if there were still legionnaires attacking your people, then you would send out your LAVs and kill a few more Romans, with a focus on surviving Roman officers, and surviving siege weaponry like their bastillae.
If they still insisted on attacking, this is when the marines might use a bit more of their artillery, perhaps a few WP rounds or napalm . Effective and terrifying. We all know how Greek fire proved to be a terrifying weapon in its day, so Napalm/WP can also be a terrifying weapon.
If a few foolhardy survivors (perhaps ~5000 at the very most?) insist on attacking again after your extensive destruction of the Roman Army in various terrifying ways, and are relatively close to your fort, then you would use your mortars, artillery, tanks+canister rounds, LAVs and other heavy vehicle weapons to thin out the crowds. Also, you could use APOD and MCLC rockets to very quickly eliminate large groups of soldiers moving on roads.
If they still keep coming, and are at the walls of your base, then you stop them by running them over, using machine guns, grenades, claymores barbed wire (i.e. your static defenses) and finally you shoot them with your rifle.
Thus endeth the hypothetical war.
That Question must have been spawned off the film Final Countdown and Samurai Warrior ...
So when is Guns of the South hitting theaters?
Who of your presidents will put his name on this operation? Will ancient Rome be added to the countries forming the "axis of evil"?
Congress would agree to call it Operation BushSuckedButObamaRulesButObamaSucksTooOKWeAgreeOnAName II.
No, they would call it something like Operation Infinite Argument MMXCII
The problem will be intelligence.
Whatever historical records we have was written by a few. (Seneca, Pleny the Elder, Pleny the Younger)
We may know what's going on in Rome, but have no idea what will happen next.
Food is an issue.
A typical Roman would put themselves up for slavery to ensure a daily meal. And the food you had was not the greatest, meat was scarce,
tomatos, chilies, potatoes have yet to be introduced. The spices from the east have yet to be introduced until the Crusades.