Trukks!
First of all, you should take 25-30 slugga or shoota boyz in a mob, not 20. It isn't that much more, point wise, and infinitely more annoying to enemies. Also, I feel that shoota boyz work better in the 30 man mobs, and slugga boys work better in trukks.
Yes, you need trukks. Large groups of orks can work very well, but against armies geared more towards shooting, or moving around quickly, you'll need trukks to move your guys around the battle field. Large groups of troops, running towards the enemy, known as 'footsloggers' by 40k, are also effective in many situations, but you need trukks to get smaller groups of orks over to the enemy quickly.
Look at it this way: the turn starts with your orks loaded in a trukk that has the 'red paint job' upgrade. The trukk can move 13in and still unload its passengers. You unload the orks to the front of the vehicle, up to 2in away (which technically gets you another 2in closer), and then you can assault 6in into close combat. This way you can move 21in into combat in a single turn, which is incredible. Also, once per game you can 'WAUGGGGGHHHH' and get another d6 inches of movement, instead of shooting (the full details are in the book). This is a possible 27in of movement in a single turn. If your guys were walking, that could take most of the game, and if your opponent keeps backing up, they may not make it at all.
The problem with only using trukks is that they can't take many casualties before dying. 30 orks, especially when backed up by a warboss and nob, can last forever.
Also, no matter what type of troops you're using, always include a nob with a power klaw. It may seem like a hassle, but when you wind up in close combat with walkers and monstrous creatures, your regular boyz aren't going to be able to hurt them. A power klaw doubles the strength of your nob from 4 to 8, and if you charged, it increased it to 9. Just keep in mind that they always strike last in combat, but with one of those in every unit, you'll be able to kill anything your opponent throws at you. There's some arguments going on as to whether or not the nob of a shoota boy squad can take a power klaw or not, but all evidence I've seen so far says they can (for instance, the sample army in White Dwarf magazine had a shoota boy mob with a power klaw in it).
No matter what, you always want your troops to assault the enemy, not the other way around. Orks usually win though volume of attacks, not quality of strikes. By being the side that starts the fight, each ork gets +1 attack, +1 strength and +1 initiative for the first round. This is often the difference between victory and defeat. A favorite strategy of mine is to keep a trukk full of boys hidden behind terrain, back towards my side of the board, so that if one of my teams gets attacked first, my hidden team can race over and join the fight next round, attacking first.
The other units in your army should be there to help shoot down the enemy, destroy tanks, and kill the annoying distant targets that give your troops trouble. I'm not too fond of Kommandos myself. They can help, but only in certain situations. Frankly, there are many other units that will help better.
Warbuggies are invaluable. They're really cheap, point wise, and if you give them rokkits (which you should), they can take down vehicles 4x their cost, by sneaking around and shooting at their backs and sides. They're very vulnerable, however, and will most likely die, so you should only field them in teams of one, so that if they're shot at, the most your opponent can kill is the one.
Bikes are very versatile, as they're good in both shooting and close combat. They can be a bit tricky to get used to playing, but they can shoot an incredible number of times, and are very difficult to kill. You just have to be sure to keep them hidden behind terrain, so they aren't shot. Also, they can be rather expensive, point wise, and their tendency to get shot means you probably shouldn't field less than 6 at a time (and 9 is definitely better). This will run you 225-260 points though, so I only use them in army lists of 1500 points or more.
Lootas are very good at shooting, burnas are great at killing infantry, and tankbustas are very good at fighting tanks, but you have to keep in mind that they are all vulnerable, and have to be used carefully.
Looted wagons and Battle wagons can transport those units safely, shoot up the battlefield a bit, and provide cover for the units behind it, although looted wagons are a bit vulnerable (for vehicles) and battle wagons are very expensive. On the other hand, battlewagons are as tough as imperial tanks, and looted wagons only cost slightly more than the buggies.
As for HQ's, I wouldn't use the warboss. Even though they're tough, they're slow and not that much more effective than a nob. Mega armor will make him more tough, but even more slow. Remember, you can't kill what you can't catch.
A warboss on a bike is nice, as he can join a bike mob, or run around on his own as an independent character. Just like with the other nobs, he works best with a power klaw.
The big mek with the shokk attack gun is powerful, although a bit unpredictable. He fires huge blasts, like a tank, but it might backfire and hurt your own side.
Mad Doc Grotznik is great for attaching to a 30 man team, but again, he can be a bit unpredictable, as he and his team ALWAYS moves towards, and assaults, the nearest enemy, regardless of whether you wanted to or not.
Ghazghkull is great for many reasons, but he costs a lot of points. He's probably worth it though.
In any case, you should explore your options, but if you're starting, I'd avoid using kommandos, stormboys, or mega armor. Those are specialty units, mainly used to replace normal troops.
For the elite, fast and heavy choices, you should take units that are good at shooting, and that can deal with the faster, more distant enemies.
Here's what I'd take for a starting 500 point army:
HQ:
Big Mek with Shokk attack gun (95)
TROOPS:
29 shoota boyz w/2 rokkit launchas and nob w/pk (229)
Trukk w/11 slugga boyz and nob w/pk (141)
FAST:
Warbuggy w/twin linked rokkit launchas (35)
Strategy: hurl everything you have at them. Keep the big mek by himself, hitting the enemy's vehicles and distant units. Charge the shoota boyz forward, and move the trukk forward, but not somewhere vulnerable. Have the warbuggy race up, distract your opponent, and try to take out the enemy's most vulnerable vehicles/targets. During the second turn, race the trukk forward and get into close combat, using the WAUGGGHHHH if you have to. Continue moving the shootas up, firing at anything that stands up to you.By now the warbuggy is most likely dead, but that's okay. Your slugga boyz have won combat (unless something went horribly wrong), and the shoota boyz are charging forward to mop up whatever the shokk attack gun left behind.
A 1000 point version of the list would look like this:
HQ:
Big Mek with Shokk attack gun (95)
TROOP:
25 shoota boyz w/2 rokkit launchas and nob w/pk (205)
25 shoota boyz w/2 rokkit launchas and nob w/pk (205)
Trukk (red) w/11 slugga boyz and nob w/pk (146)
Trukk (red) w/11 slugga boyz and nob w/pk (146)
FAST:
Warbuggy w/twin rokkit launcha (35)
Warbuggy w/twin rokkit launcha (35)
ELITE:
5 Tankbustas (75)
HEAVY:
Looted wagon with hard case and two big shootas (55)
I'd start with the game with the tankbustas moving inside the looted wagon (but they shouldn't start the game inside it, that's too risky), and then having the wagon charge forward, to both provide cover and intimidate the enemy. Besides that, the strategy is basically the same, and I've found works well.
Of course there's a lot of strategies out there, so find what works best for you.
