First things first:
That would be a dead giveaway, so going to suggest that you have clothes and equipment in piles, or all mixed up in one grand pile. A holy symbol is a dead giveaway for any cleric, and it's not exactly fair to the others if you give them that--same deal with something like a lock pick set. This will make things easier or more difficult depending on what they have.
Stats. The toughest ones that I see here are Charisma and Intelligence. If they have a score lower on Intelligence or Charisma than the player actually has, how can you enforce if they will come up with something or not?
Your descriptions of HOW they are thinking will help.
I say that you give each of them a slip of paper with their initial thoughts and feelings, which you can ask them to open at an opportune moment--let them know that these are roleplaying cues to start with, and that they don't have to act on these thoughts.
This is stupid. These people are stupid. If I punch one of 'em, maybe they'll be less blurry.
Some sort of spell is at work. What could it be? Perhaps if I take a moment to think this through, we can figure out who is whom.
Some sorcery afoot here. But it seems all of us are in the same boat. We must work together.
Are those rubies in the hilt of that sword? Let's see, three rubies, market value 20 gold each...
Just to confuse them, they've got bits and pieces of memory--let's say the paladin was holding the lock pick set because the rogue couldn't be trusted with it. Either the paladin feels that they must have the set from the pile, or they already have it on them.
Also, describe how they see the world--it's all going to be different. Any fighter or paladin is going to do a threat assessment of any NPC they see.
Smart players/characters that get the tiefling clue will simply ask that the party take off shoes and then walk through dirt or mud. The foot prints might help with that-- this is the sort of thing a Ranger-type might come up with.
Things such as Strength and Dexterity can be tested for in mock combat, or actual combat.
Stamina will have a specific effect on things.
With spell casters, I might do this--they've already cast mage armor from before they can recall or some such, and may notice the effect when they are hit. Or they can look at a spell book and find that they can read it and memorize spells.
Races. For races, the players can't see themselves but they may have special abilities--if they tell the others, those others may have the requisite skill to figure that out--but there should be a difference between player knowledge of who has darkvision and character knowledge. The character might know they have darkvision, but might not have the knowledges to know what that might mean. It might be important for you as a DM to let the players know about that distinction. They will definitely be helping each other to understand who they are.
Philipp's example of dropping clues is an excellent template on how to handle each class--I would have notes ready beforehand with each of the classes for various situations.