The UNSC has many strengths, early game vs covenant it can be a little difficult to play against an aggressive rusher, assuming you survive you have an armada of strong units.
If you play anderson, your tech is 2x faster and 1/2 cheaper, and lets face it we all know UNSC techs are ridiculously expensive. Its easy to put out early mid game pressure with a hog/gremlin rush, specially with maps that have reactors on them. If anything use the warthog rush to buy you time to upgrade to hawks and get your vehicle depots pumping out units(on occasion i even knock people out of the game with this rush). End game you have a really strong air unit; the famous hawk, in numbers its deadly and teamed up with an upgraded cryo bomb, armies will crumble before you. watch for Enemy anti air, cryo vamps and use cobras to take out enemy wolverines. Remember Cyro Bombs (especially when upgraded) rape enemy armies, and instantly slaughter a good chunk of air units.
If you play as Forge, you have pre upgraded supply pads (which can save and produce valuable resources early on), and receive the tough grizzly and cyclops. Early on in the game you could always try a cyclops rush, it never really wins the game for you but you can kill a few buildings with them early on, aim for supply buildings, then any unit producing building. If your lucky you may even kill your opponent. If not you sure get a nice advantage on them. Assuming you survive and can come up with a few bases to mass produce expensive heavy armor, you can upgrade to grizzlies, which are tough buggers, the only direct counter to them that is truly an onslaught is hawks, But a well micro'd army of Grizzlies Cobras And Wolverines can really put a hurt on any opponent. Forge also get the carpet bomb which is my least personal favorite of the UNSC leaders power, however it can be devastating vs very clumped armies.
Next we have Cuttler. Its been said that elephant rushes work well, i wouldn't know i have never tried one, I will however tell you that parking 1 or 2 elephants outside of a battle field and pumping out extra infantry can be nice. Be warned if you do not keep your elephants back they can be easily killed under pressure. Cuttler also has the Mac cannon which can be useful in many respects; it can take out enemy armies, really hurts covenant leaders (cept the arbiter when he hops around like a dam jack rabbit) or put extra pressure on an enemy base under fire. Cuttler also has ODST. ODST are a pain in the ass to all armies, they have tons of health, regen after battle, can be hot dropped anywhere on the map, and can shoot rockets and buildings and enemy units. They aren't particulaly effective against anything however, for the price and the durability are a cheap and really annoying distraction. Lets face it, if you got all day you could even kill people with armies of ODST. Covenant jackles really are the only unit in my opinion with the power to take these bastards down quickly. Also his first base starts out fully teched saving 400 resources early on, and 300 each addition base you create.
All UNSC leaders can produce vultures, a slow moving, slow building, expensive heavy air artillery. I don't find them super effective vs large forces, they seem to get overwhelmed, however in 3v3 i've been know to sneak about 5 or 6 of these bad boys behind enemy bases while my teammates hold the battlefield, thus unleashed a heavy barrage of missiles on they enemy bases, always a guaranteed kill for one base, if not more. 5-6 vultures will take a full teched base down to about 1/3 health with missile barrage. I don't suggest this without good team support, otherwise it could be risky and chances are you would get rushed down.
Disruption bomb is also a nice move, however i feel its cool down is a bit extensive as the covenant leaders can rebuild a new leader within a minute upon death OR just port their leader back to home base and try again in a minute. This is a real pain in the ass with more than one covey player, especially in 3v3 when they try to win the game on the early end of the spectrum.
My final thoughts about UNSC, they are expensive, Slow, But with multiple bases in endgame will wreak havoc on the battlefield with a variety of combative techniques. Overall i find their Units strong and effective.