What exactly are the properties of Strangfied cosmetic items in Team Fortress 2? I am not rich enough to afford one to figure it out on my own. I also don't understand what the 'point' value on the item means. I've checked the wiki, and it doesn't describe how Strangified cosmetic items exactly function.
They track points scored while wearing that item. You could've found this in the Unique Rank Methods section of the Strange article, under "all classes/cosmetic".
You can make a strangified cosmetic item by using the respective strangifier; this is the list of items that have a strangifier. To obtain a strangifier, you need to complete a chemistry set; usually, they require drops you obtain from the Mann vs Machine mann up mode.
(Taken straight from the Team Fortress 2 Wiki - Just look at this)
Here are the following qualities (prefixes) for the items, and what they are.
Normal/Unique - Anything you have received from drops or have crafted. These are usually not marketable, but are tradable.
Vintage - Things that were obtained before the Mannconomy Update.
Genuine - Usually cosmetics, but can sometimes be weapons, but these items are distributed to users from promotions, such as the most recent one with Wolfenstein.
Strange - A quality that has a rare chanced to be assigned to items purchased from the store or uncrated. These items track kills and have a changable prefixes based on the number of kills using that item.
EDIT: A similar type of item to this are the Killstreak items with the Strange color modifier. They also track kills but have a separate prefix ladder to ordinary Strange items.
Unusual - A quality assigned to cosmetics that have a particle effect on them. These items, like Strange items are rare.
Haunted - A quality given to halloween-themed items, of which can only be used on full moons or on Halloween itself.
Collector - An item made of a lot of copies of unique versions of itself through crafting with Chemistry Sets.
Community/Self-made - This quality is assigned to items given to a workshop artist when his/her workshop item is accepted, usually attached to the item that he/she has created. Items with this quality usually are usually not tradable or marketable.
Valve - Items only given to Valve employees, like Robin Walker's OP Rocket Launcher.
What you may have been talking about are items with Strange Items, which you can more information here:
Strange items track the number of kills done with the items... And have changable prefixes based on the number of kills with the items. (The prefixes are listed on the wiki... Just scroll down a bit)