I hate early game and laning. The goal of this strat is really simple, pick strong early game champs, get an early advantage, then 5 man push top win or lose.

Why top? Because while top laners usually have good sustain, they typically lack good AOE needed to stop a push. Also, most teams are bot-side heavy for dragon control, making it very difficult for the enemy to react quickly to the push.

Get your starting items and immediately head to the river in top. Most champs should wait to get their first skill depending on whether or not a team fight happens.

You have two smites (3 with Nunu's consume), so you should be able to take top-side wraiths, then both red and blue buff. If the other team is bot-side Blue, chances are they won't see you at all. Blue buff goes to Taric (that heal spam), and Red goes to GP (that Q proc). Once you have the buffs, next step is five man gank top!

This should be really simple. In theory you are showing up a little late top, and they are probably in the middle of the wave (most are melee). You have an exhaust, an ignite, lots of CC, and TONS OF DAMAGE. They should die. Congrats! You've now reached the pushing phase!

OK. So the enemy top is dead. You have both RED and BLUE buffs. Now you push HARD. Almost every champion has insane attack speed or damage early. That tower will go down fast. So on to the next one, and the next! With three smites, three heals, a promote, and so much damage and sustain, you should be able to sustain the push all the way to the third tower. Once you get the top inhib, it will probably be extremely hard to push the Nexus. At this point you will have to be flexible with your strategy and adapt to the enemy champs.

Here is why these champions are perfect for this. They have the CC they need for that lvl 1 fight. They are almost all extremely tanky early. They are also all great junglers (that lvl 1 jungle clear is important). They also have great dmg or scale off auto-attacks. Finally they are all able to heal themselves, and sometimes their allies.

Mundo
Why Mundo?
Spammable slow
Huge early attack damage (highest in the game) over 120 dmg at lvl 1
Built in regen
He is essentially the carry. Build dmg and knock out those towers.

Tips:
Always have E up when attacking towers.
Use your ignite for LVL 1 gank. It gives you bonus attack dmg.
Save your surge for a time when you can get its whole duration on a tower.

Taric
Great stun for small skirmishes (lvl 1 teamfight or gank, solo tower defender, etc)
Armor aura (tower dmg now tickles)
Spammable heal! The CD is reduced with autoattacks, so attacking a tower means more heals, plus blue buff and clarity take care of any mana issues. No one on your team should ever stay low on health!
Armor reduction - great being your teams dmg is almost all physical.
That Ult! No better way to take down towers fast.

Tips:
Use your stun to setup ganks.
Always heal an ally when possible.

Nunu
Another spammable slow. No one can get away.
A built in smite. Super fast pusher and jungler.
Self heal.
Blood Boil! Keep it on mundo for tower damage, or on someone that needs ms to escape. This should always be on someone!
Auto attacks mean free spells. Attacking tower is easy autoattacks and means you shouldn't have mana problems.
That ult! Channel it under a tower and the enemy may have no choice but to run and leave it undefended.

Tips:
Use consume and smite on blue buff lvl 1 so Taric can grab it right away.
Always keep blood boil on Mundo when attacking a tower. Otherwise use it to help someone get away if they need to.
You should be a meat shield and should be willing to die first if necessary.

Alistar
Perma spam AOE heal. Insanely high regen for all.
Lots of CC.
Headbutt keeps dangerous targets far away (or makes for an incredibly easy kill).
Very tanky.
That ult! %Dmg reduction and 60 attack dmg? Perfect for tanking tower hits and beating them down.

Tips:
Spam your heal at all times. UNLESS YOU ARE UNDER A TOWER AND A CHAMP IS NEAR YOU.
Don't draw tower aggro with your passive unless you need to save a teammate.
Headbutt is great for ganks, but in this strat its primary purpose is to keep enemies away.

Gangplank
AOE Speed Boost and Team Dmg buff. Great in jungle and for pushing towers.
Stackable slow.
Spammable Q.
Absorb CC for the team with oranges.
Can ult to defend towers or deter defenders.

Tips:
Get Red Buff Lvl 1 and use it for the gank.
Use exhaust both offensively and defensively.
Spam the team buff as much as possible.
Q harass when you can get away with it (tower won't hit you).