Here is my short research into slingshot regulation in OR.
A slingshot is considered a weapon as defined in 166.360 Definitions for ORS 166.360 to 166.380.
(b) Any dirk, dagger, ice pick, slingshot, metal knuckles or any similar instrument or a knife, other than an ordinary pocketknife with a blade less than four inches in length,
Oregon is an open carry state, so you should be able to carry it openly just as you would have to do with a knife over 4".
166.240 Carrying of concealed weapons.
(1) Except as provided in subsection (2) of this section, any person who carries concealed upon the person any knife having a blade that projects or swings into position by force of a spring or by centrifugal force, any dirk, dagger, ice pick, slungshot, metal knuckles, or any similar instrument by the use of which injury could be inflicted upon the person or property of any other person, commits a Class B misdemeanor.
This drives home the cannot conceal part.
Not a lawyer, but I would assume you can transport your slingshot(s) in a locked box/bag as you would a firearm. This is where it gets irritating for me because I assume most law enforcement does not care about your daisy slingshot concealed in the box you purchased it in between the store and your home. But it sure gives them something to use if they want to get you on something. Would love to get some official instructions on transportation of non-firearm weapons, because there doesn't seem to be any official guidance. I think once it is off your person it could be kept in a backpack, but once you pick it up it becomes concealed? So I don't know, I guess if you are transporting you slingshot collection you need to either hang them all around your neck or put them all in a locked container?
On top of the state laws you have to pay attention to local ordinance. Most Cities prohibit shooting a slingshot inside city limits. I live in Hillsboro OR and we have a "Beanshooter" law that actually prohibits sales of slingshots, although it is not enforced as I can buy a slingshot at any sporting goods store.
No person may sell, offer for sale or use a beanshooter, sling, or similar device or article.
So it looks like it is not on the list of ways to take game on the ODFW website
. But from some short research I saw comments to the effect that it is possibly legal to take game that is not regulated, and thus does not provide a list of legal hunting means, with a slingshot.
are not covered under the game mammal, furbearer, or sensitive species rules. For unprotected mammals, there are no closed seasons or bag limits. However, a hunting license is required and all hunting regulations still apply."
Since they never applied a list of "Legal Hunting Methods" for unprotected mammals then there doesn't appear to be any restriction.
This represents the best of my knowledge, and my best guesses. If you have any other info, that would be great.