Oxfam is headquartered in Nairobi, Kenya because it's a relatively stable/safe country with relatively good facilities and infrastructure. Nairobi provides a good central location to reach other parts of Africa where much of their work is based, and Kenya also provides a favourable regulatory environment for these international organisations to operate. The UN Environment Programme (UNEP) is also based there.

Both of these organisations certainly have their issues with corruption, fraud, and grift, but that would likely be the case no matter where they are based. If anything, being physically closer to where much of the money is being spent should help them keep a closer eye on the work that they're funding.