http://paizo.com/rpgsuperstar/faq#v5748eaic9snv
"Can I refer to Pathfinder campaign setting material, such as nations, heroes, or gods in our contest entries?
Yes, but keep in mind that not all of the judges work at Paizo or have a strong knowledge of the campaign setting, and some of the voters may not have the same breadth of knowledge of the campaign setting. Contestants hoping to get an "edge" by including a bunch of Pathfinder and Paizo-related inside jokes may find this inclusion could be detrimental to voter preference and round results."
Sounds like you can but it's playing with fire.
I think you're talking about two different situations.
In your second example, you start giving the item some back story. If you look at the core rulebook, we all know the holy avenger is meant to be used by paladins, but it doesn't come out and say that. It just tells us that it's more powerful when wielded by a paladin.
Now, if you want to tie your item into Golarion, that's more OK, but you need to do it a little more subtly, I think. For example, you could have a mantis sawblade saber that gives a bonus to assassination. People who know Golarion will likely recognize the tie-in there, but you probably wouldn't call out that the mantis sawblade saber was made for/by red mantis assassins.
As Moik quotes, you want to make sure you're using the campaign setting correctly. The judges know the campaign setting, so they're going to know if you're not playing in it correctly. You're also taking the risk that the voters will know the Golarion lore you're referencing too, so I'd personally veer away from that choice, but if you can hit the mark, that's great.
For some examples, look at the night monarch vardo (which had a really subtle tie-in) or Cayden's cup, which was pretty explicit about using Golarion lore. (Huh, didn't realize that was your item, Andrew. Nice...)