Tactics

mkill goes into far more detail than I do in his Art of Striking thread. Read my little intro below, but then follow the link to his guide, and read it multiple times. This discussion is, once again, heavily filtered through the "striker" lens.  Auspex7 has a nice thread referenced in the intro about how to get your Pursuit Avenger to work as an off-tank.  This page here is not that discussion.  This page is how to get your Avenger to kill things as quickly as possible.

Make them misbehave 

Your censure is structured as a rattlesnake power: "Hey, look here monster.  If you misbehave, I'll do something you don't like".  You'll usually get better DPR if you manage instead to get it to work like a spider power ("Heh.  You fell into my trap, monster").  To do that, you need to make the attractiveness of "behaving" go down.

If you Chase, you WANT them to run. Put up damage auras around you, or darkness clouds. Tell the fighter to not mark that guy, but tell the Paladin, Swordmage or Warden to mark them and kite them. Move away from melee brutes so that they don't provoke an OA from you, if you're better off with the bonus. Go after artillery that would provoke if they attacked you, and make sure your OA is good enough that they avoid it. Don't box your target in.

If you're a Martyr it's usually pretty easy. Go early, run into the middle of the pact and watch them all beat on you. Push everyone away except your oath target (Divine Rage, teamwork), and then vaporize your target. Repeat. Provoke OAs to get your position just right. Say hello to all the minions... at low levels it can hit you for 4 damage, say, and give you a +4 bonus to all your attacks until the end of your next round. Your main concerns are surviving the beating without going through surges too quickly or using up your groups healer.

AndrewRF put together a nice list of ways for a retribution avenger to chase down/lock down it's target (Divine Power has added many more). Ignis_Fatuus followed up with a long list of tactics and powers for a pursuit Avenger to convince it's target to run. Both of these are well worth a read.

Get Multiple Attacks 

If the monsters are misbehaving, you should have some really high static modifiers.  The best way to abuse those modifiers is to get multiple attacks while you have them. 

You only have a couple powers that qualify (Fury's Advance is the first), so you need items, or team work. Convince someone to be a Warlord, Bravado if possible, with Commander's Strike. You want lots of attacks, to apply multiple times per round those lovely lovely static damage modifiers you've accumulated. Mutli-class to grab powers, or PP with powers. Pick up some equipment... something.

Take chances 

You've got a pretty good AC. You've got more HP and surges than most strikers. If your target moves away, go after it. Take the OA. It's all good. If you get hit, just funnel that rage into beating up your target.

I've pointed out lots of feats and magic items that help survivability on the assumption that you're taking a lot of risks. If you have all that survivability and don't take risks, you won't help your party out any.

Remember that the leader is a group resource 

Particularly for Martyrs... Don't monopolize your group's healer, and don't run out of surges. Prefer resistance and regeneration to the ability to spend a surge, and manage your AC so that you can stop getting hit when you've decided you don't want to spend more healing.

If you are a Martyr, you might want to be hit, but you won't want to be hit regularly. A few times in one round is perfect: you use your action point, you get the chance to use your mutli-attack powers at peak effectiveness, you may get given extra attacks. But getting hit round in and out will just suck out all your groups healing abilities. So make sure you can turn off the "go ahead and hit me" tactics.

Concentrate on positioning 

You need someone to misbehave to get the big static bonuses, but you need to isolate your target to get the oath. It can be tricky to get both, but you'll want to. Delay and let your fighter or warlord move some people around? Use your mobility to get around the target? If none of these work, well, you have some powers that will make everything ok ... but only a limited number.

Choose who to abuse correctly the first time 

You can't mess this up much. Once you pick an enemy, you're gonna be stuck hitting them until they die. So get it right. Look for the annoying squishy targets and nuke them first. If they're squishy they're more likely to misbehave, so that's all for the better.

Save the big guns (the debuffs) for the solo/elite, and save him for when your party can focus fire... cause a debuffed enemy won't last long.

Play well with others 

The basic mechanics of the Avenger class tend to suggest a "solo duel with a key bad guy" mechanic. Um, screw that.

If you're in your line, it's harder for monsters to deny you your oath. If you're applying status effects, it's nicer to let others work with them. If you're a crit fisher and you'd like to really ruin a monster's day, it's nicer if the leader can boost your to-hit or damage. Those "woodshed" powers? The woodshed is actually the square that's next to the Fighter/Ranger/next Melee Threat. So, work with your party. They'll like you more, and you'll like them more. So you can't claim quite as much glory... ah well.

Some Math notes 

The table below lists the probabilities (rounded to 2 decimal places) of getting a roll of X or above, if you can use your Oath and have fair dice.

There are a few of things to take away from this:

This doesn't mean that +1 and +2 effects don't matter. They do. They just don't matter quite as much for you as others. Instead of hitting with a 10% higher frequency, you hit with an 8% higher frequency. Or even a 6% higher frequency if you're well over 50/50. Or 13% if you're fighting things you might not want to be fighting.

This math is also why there is all the focus on critical hits. If you are fighting your Oath target and only crit on a 20, you crit as frequently as someone else who only needs a 19. If you need a 19 (Hand of Divine Guidance,Radiant Servant, Draeven Marauder), it's as if you needed a 17. If you need an 18 (various AP features, usually), it's as if you needed a 16. And if you need a 17 (Raise the Stakes) you'll crit on every third attack.

So feats and powers and equipment that assume that a crit is something that happens once an encounter are much more effective in your hands, especially if you make any effort to improve your crit range.

So I crit. Now what? 

Some things that can trigger off of a crit. Or why I care more about crit range than just size of the weapon. I don't think this list is comprehensive.

Feats

Equipment

PPs

EDs

Powers

Rules Notes 

If you have a feat or power or feature that has language like "when you score a critical hit with a radiant power", that rules element is keyed of the radiant keyword.  Which raises the question, how can you get more of your powers to have the radiant keyword?

Well, obviously you could choose powers with the radiant keyword.  You have many choices.  However, if you do that be careful of Frost Weapons.  Elemental weapons like the frost weapon turn all damage done to the appropriate type, which means they take off all other keywords.  (This changed in the April or March update...). Another approach is to simply use ''Painful Oath''.  As of these two CS replies, Painful Oath and other forms of "extra" damage add keywords.