I'm not sure about the UN, but many charity organizations (including the Red Cross) do not accept private donations of goods/clothes. They simply don't have enough volunteers to manage the admin, storage and transportation that comes with it. 

Here are some ideas what you can do with your clothes:

- Salvation Army. I'm not sure about Geneva but generally they collect clothes for homeless people. I'm not personally a big fan of the organization because of their position on gays, but you may feel different.

- Boxes at recycling places: Throughout Geneva at recycling places there are containers where you can leave your clothes. I'm not sure where they go, but it's easy to drop your stuff in there. Put your clothes in plastic bags before you put it in the container. 

A few leads.

For Syria, you might try contacting Tawfik Chamaa, a Geneva-based doctor and spokesman for the Union of Syrian Medical Relief Organizations (UOSSM). Otherwise there is a specific charity org SAWA (Syrian american women Charity association) www.sawa.org which when you email   help(at)sawa.org will give you possible collect stations in Geneva or Switzerland.

For Gaza strip, try info(at)howgaza.org which in cooperation with the House of Wisdom Institute coordinate on to Charity Organisations from Bairut.