My understanding is that, in order to hear the correct dhamma, one must hear it from somebody who displays the outward marks of humility, generosity and selflessness. Otherwise, one cannot be sure one is hearing the correct dhamma.
The correct dhamma is related to the teaching rather than to the quality of the speaker. For example, Christianity often preaches about humility, generosity and selflessness but obviously has a different dharma (teaching) than Buddhism.
Are there any Buddhist organizations or monastic orders that teach dhamma to lay believers
Yes. Buddhism Stack Exchange and Dhammadhatu is most beneficial.
and do humanitarian work, either in poor countries
My impression of Buddhist countries (such as Thailand & Burma) is, prior to Western contact, there was relatively little need for 'humanitarian work' because, despite inequities, most people had sufficient requisites of life. For example, Thailand is not a country historically known for poverty and it is well-documented Burma was a country of great domestic abundance before the British raped & pillaged it economy & politically.
I think an examination of history might find 'Christian humanitarian charity' goes hand in hand with Western (Christian) colonialism & exploitation. For example, while I know little about if British colonialism contributed to poverty in India, I do know the British created a man-made famine in Bengal during WW2, which killed around 2 million Indians. Even my own father immigrated to Australia because of the poverty Britain created in his country of birth.
I'm thinking things like refugee resettlement
Despite your obvious good intentions, refugee resettlement is generally the addressing of a symptom rather than the addressing of a cause. For example, in my lifetime, there have been Vietnamese, Lebanese, Palestinian, Iraqi & Syrian refugees in my country of birth, each caused by American wars (directly or indirectly) towards those peoples.
It is well-known in Western history Christian missionaries quickly followed Western conquerors, which includes in the recent Iraq War.
Despite your obvious good intentions, you appear to be imputing a Christian Western Semitic paradigm onto Buddhism.
Unlike Judaism, Christianity & Islam, Buddhism has no doctrine of imperialism, conversion, world salvation & world conquest.
addiction treatment and recovery
In Thailand, there are lots of traditional addiction treatment and recovery using traditional herbal medicine, where monks are involved (even though Vinaya appears to forbid this), such as Wat Thramkrabok
fundraising for medical research or vaccination drives, tutoring special needs children, etc. Can you recommend/provide links for your "favorite" organization?
Again, despite your obvious good intentions, you appear to be imputing a Christian Western Semitic paradigm onto Buddhism.
Each nation has evolved, slower or quicker, technologically in its history and each nation obviously does its best to advance what Buddhism calls the "four requisites" of food, clothing, shelter & medicine. This said, while Buddhism clearly teaches medicine is a human life requisite, it is not the role of Buddhist monks to develop medicine and medical technology.