I've been a national officer in my NPC group. The things that you listed are the types of things we would offer to members and then toss out if they weren't taken. They have no "street" value.

Honestly? If it comes down to it, and you've made every good faith effort to find an appropriate resolution for the group's property, I would dispose of the items. If at all possible, I recommend you retain the scrapbooks and photos. Is there any chance they could be stored in a relative's garage?

As for the rest of the stuff, it's not of any particular historical or monetary value. Once you've exhausted all other efforts (attempting to Facebook alumnae, etc), I suggest donating it all to someplace like Goodwill. Obtain a donation receipt in the name of the sorority and keep it in your files in case you need to explain yourself later. Do not use the donation as a personal tax write-off. If I understand you correctly, you are the last remaining officer of this organization. It sounds like you are the only authorized individual left to make a decision. Similarly, if you have any money in a banking account, you can donate the money in the name of the sorority to your sorority's preferred charity and then close the bank account. Again, keeping the donation receipt to prove that you appropriately managed the money to the final closure.

Without knowing the particulars, I am saddened to hear that the other sororities voted "no" to letting your organization participate in recruitment.

Best of luck to you.

Donate the last three items on the list to a charity; someone can use those. Possibly the 3 boxes of shirts too.
Many schools have an alumni FB group. Post something on these about the other items to see if there are any takers.

If it doesn’t have letters on it or isn’t sorority specific give it to Goodwill. The other stuff, keep trying to contact alumnae via the methods I and others mentioned.