Yes I believe that Oxfam do give aid, they are not a form of aid but they do give aid. It's called voluntary aid. There are different types of aid:
Official government aid- Given by a country
Voluntary aid- run by NGO's (non government organisations)
Bilateral aid- one country to another
Multilateral aid- Provided by a group of countries e.g UN
Short term emergency aid- provided to help cope with unexpected disasters
Long term aid- directed to continued improvement to quality of life (aid given to abolish problems such as hunger extr.)