Kartissa's page

Simple answer, ignoring all the rules on polymorph and transmutation:

Animal Growth grants size bonuses.
Form of the Dragon grants size bonuses.

The spells don't stack.

Using Smite Evil to cheat won't work. Because when you try to smite him, you will find out you no longer have the smite evil class feature. Or your spells. Or Lay on Hands.

Good luck with the Ogre, Mister Fighter-Without-Bonus-Feats.

Depends on how your GM defines the Paladin's code. Using Smite or LoH in a 1-on-1 non-magical duel isn't necessarily an evil act, especially if the paladin intends to save lives by doing so. (Especially if the Smite actually works, which raises the question of the other side of the Ogre's alignment. The default is Chaotic, which means that it probably wouldn't hesitate to cheat if it had to....) In fact, cheating in this instance would likely be a Chaotic act, for which there are no lasting repercussions.

The Code of Conduct section only mentions losing Paladin abilities if he willingly performs an evil act. Granted, the following paragraph refers to not lying or cheating, but it also mentions punishing those who harm or threaten innocents. (I'm assuming the people the Paladin is trying to save through this duel are innocent....) I actually have a problem with this paragraph, since by a strict interpretation, the Paladin cannot feint in combat (lying about where he's going to strike) or use flanking attacks (must act with honour, and ganging up on somebody could be considered dishonourable, especially if the target turns away, and the Paladin is now effectively stabbing it in the back!), neither of which seem to present any problems for most GMs.

(As an aside, if the Ogre tried to Intimidate the Paladin, would that cause the watching crowd to cry foul when the (Su) Aura of Courage activates, making Pally immune?)

I'm fighting an ogre that has above average stats and possibly a brawler level. So, he's either CR 4 or 5 and I'm fighting him alone. I'm level 4 and at a disadvantage already because I can't use any of my paladin combat bonuses.

If the Ogre's that tough, you're not really expected to win in a 1-on-1 fight. Challenge ratings for combats are typically based on a party of 4 or 5 PCs. You have an effective party level of 3 (level 4, reduced due to fighting solo), so it is possible for you to win, but not without using all the class abilities you have at your disposal. (You may want to point all that out to your GM if he's that inexperienced....)

Now, on to the question of detection:

1) Since Smite Evil has a lasting effect (deflection bonus to AC), I would say that it can be detected in a similar manner to Shield or Mage Armour.

2) Lay on Hands channels positive energy in a similar manner to the various Cure spells. Since they can be detected as they are cast, I would rule Lay on Hands can also.

In both cases, they would be considered a nonspell effect to identify what they actually are (DC 15 + 1/2 caster level).

Sorry, but it looks like you're probably going to lose, unless you can persuade the ogres that it's not a fair fight unless you can use your divine blessings and/or Enlarge Person to even the odds. Or unless your GM is kind enough to use the default Ogre profile with no advantages, since that's only CR 3.