Leadership 2

Given that the Orcs and Goblins army was the first army of 7th edition, it is understandable that has fallen behind the times as far as the gaming power curve goes. Demons, Vampire Counts, Lizardmen are all greatly overpowered comparatively.

Can Orcs and Goblins even compete against these lists?

Let's discuss... starting with the Lizardmen.

There are 2 main builds you need to worry about these days: Slann and Oldblood/Carnasaur.

Slann Mage Priest
Pretty much every Slann you'll run into these days is better than the old 2nd Generation "uber" Slann of last edition.  The Focused Rumination (+1 Power Dice/spell) is ubiquitous, as is Focus of Mystery (knows all the spells for any 1 Lore).  Cogitation is also quite common, and REALLY fucks with level 4 wizards (choose 1 enemy wizard w/in 24", who ignores all 6's to cast).  Since you'll be packing a L4 Shaman, make sure you keep him >24" away from the Slann at all times.  Greenskin magic has an advantage here over most other lores in that it really doesn't care that much about range... so you can afford to keep your spellcasters at a safe distance.  The Slann is almost always accompanied by a large unit of Temple Guard.  Never, ever engage this unit.  Even if they baited you with a juicy flank.  It's a trick, don't do it.  Magic heavy Greenskins simply don't have what it takes to chew through Temple Guard.  Use fast cav, single Trolls, etc to occupy this unit's time.  Never engage it with anything worth points.

Oldblood/Carnasuar
Is now a totally viable Lord choice.  It's no longer a large target (so it can do stupid things like hide behind a unit of Skinks...), does D3 wounds to EVERYTHING, is S7, and can join units.  Keep in mind that even when it's joined a unit, if you can draw line of sight to it, you can target it separately with magic/shooting (it's US5+).  It still becomes Frenzied (and so does the Oldblood) when it makes its first kill, and this may be the best way to deal with it.  Throw it something soft and inexpensive like Wolf Riders FC, even when it's deployed in a unit..  It'll obliterate them of course, but now it's frenzied and can be lead around wherever you like, hopefully well away from anything worth real points.

Other things to be aware of:

Engines of the Gods
Pretty much every LM army will be packing at least 1 Engine of the Gods... the douches will have 2 or 3 (and feel free to gack their composition accordingly).  They're truly ridiculous: Uber Stegadon that makes the Skink Priest riding him into a virtual level 3 wizard, can do 1 of 3 things at the start of each magic phase (that can't be stopped in any way): 1) ALL units w/in 12" get a 5+ ward save vs ranged effects. 2) Make all the spells for a single Lore easier to cast by 1. 3) ALL enemy units w/in 2D6 inches take d6 S4 hits with no armor save allowed (S5 against undead and daemons)... this is the truly mean one, though the others are good too.  Bolt Throwers, Doom Diver, and S6 greenskin magic are yer best answers.  If you have a combat character who's capable of killing the Skink Priest in combat (the Skink has a 2+ AS, but is otherwise gimp) send him in asap.  Once the Skink Priest is slain, the EotG is just a big Stegadon (still good mind, but the uncounterable effects are what make it retarded).

Terradons
Are no longer the combat beasts they once were, but their Drop Rocks effect is pretty frick'n good.  Usable 1/game, if even a single Terradon model flies over an enemy unit, the whole unit of Terradons can drop rocks, doing 1D3 S4 automatic hits/Terradon.  As of a recent FAQ, they can even do it during a charge, assuming they fly over another enemy unit on their way to the charge target.  They can fly through forests too.  Their super squishy though, and don't count as skirmishers for the purposes of shooting (they're US2 each) so they're easier to shoot down than most flying units.  Concentrate fire, magic and mundane, before they get a chance to drop their proverbial load.

Salamanders
Are some can of ass-whoop against Greenskins.  They are basically walking Dwarven Flame Cannons (though they're S3, -3AS instead of S5).  They look like breath weapons, but aren't, so don't let your opponent try to march AND shoot on the same turn (the most recent FAQ cleared this question up quite succinctly).  The real problem for Greenskins is that any unit which suffers a casualty from their flame template takes a panic check.  Deal with them the same way as the Terradons: they don't count as Skirmishers for the purposes of shooting either.  Bolt Throwers, bows, magic missiles etc.