"Fight evil" immediately became a problem. If you swear an oath to fight evil, then the character is forced down a single path where she must fight. She has no other options or tools. The results of her actions could increase the misery of those around her. Even if she accomplishes evil herself, she must go there because there is the only place that she can go.
Looking at oaths in general, paladins usually swear to do multiple things. All parts of the oath must be kept or she loses her status. So she lives in a world where all things are artificially made equal.
What's really missing from most paladins is a mechanism to handle internal, moral conflict. That seems odd as paladins are people of rules and laws, yet that is the case.
So here, I'll sketch out my basic moral toolbox for resolving paladinish conundrums.
1. Increasing good trumps opposing evil. As the universe is inherently evil, there are an infinite number of evils to oppose. Evil is cheap. In contrast, opportunities to increase good are few and precious. It is better to labor for gold than dirt.
2. Immediacy trumps possibility. The problems of there here and now need solving over the problems of later or far away.
3. Large impacts trump small impacts. Not all problems are equal. Paladins don't have the luxury of being able to pick how and when trouble appears, but they can decide which problems they will engage.
4. Diplomacy trumps violence. Violence triggers cycles of vengeance. A paladin seeks to end those cycles.
5. The present trumps the future. You'll eventually die. You must trust the future to look after itself. Someone will be there when the time comes.
6. The least bad trumps the worse. In this world, you don't always get easy options. In a moment of crisis, you will make the best possible decision that you can be made. Someone else may make the decision.
So, let's use these principals to talk about orc babies. This particular problem is the most famous paladin-screwing scenario. So, let's examine the case with the principals above. You just killed an orc tribe. There are some orc babies. What do you do? This is where the so-called "fun" debate begins.
- If orc babies are killed, the overall increase in good will be negligible. You've already killed all the grown-up orcs. The babies could grow up to attack again, but that's tomorrow's problem. The immediate problem is whether to slaughter non-combatants.
- If orc babies are killed, the overall lessening of evil will be negligible. In twenty years, nobody's going to notice or care about a handful of orcs.
- If the orc babies are taken to an orphanage, they will likely get smothered in their sleep or get raised in a society which hates them. Not only that, if they escape to orc society, they won't fit in there either. If not outright evil, it's certainly a horrid thing to do.
- If the orc babies are ignored, you've shown mercy, which increases the good in the world. They may still grow up to kill people, but that's tomorrow's problem.
As you can see, the only option which produces any good is to ignore the orc babies. However, if there are no caretakers left living, leaving them to starve would be pretty horrid, so it would be more merciful to kill them outright.
And if your party outvotes you and decides to kill those babies? The least bad trumps the worse. You worked toward your goal but you lost the argument. You're now in least bad territory. Have the decency to kill the orc babies swiftly and then bury them properly. You should even volunteer to do the deed, as you won't be killing in anger or hate.