I recently posted a photo of myself with a couple of Papuans in native getup and many people were asking 'Where the hell are you', etc. To simplify answering everybody and organize my thoughts I'm putting down this.
Where was I
I am in Indonesia, province called West Papua. Inside it is the Baliem Valley. It was completely unknown to the outside world until WW2.
Ie the people living there have been cut off from civilization since before civilization started - for the last 45,000 years.
Why did I go there
Because it's there.
It may be fast becoming just like any other third world locale, but still - visiting a place that didn't exist to the outside world until WW2 is pretty damn cool.
Do they always walk around like this (ie naked and with gourds over their cocks?
The almost butt-naked look is their national dress (ie like a вышиванка или кокошник). It's not worn outside of special occasions.
As far as I understand it was fairly widespread until 1970s-80s when the Indonesian government (which colonized these people in 1960s) had an anti-gourd campaign, effectively banning it (as it was seen as backward). Any papuas you meet on the street will wear regular clothing.
Most pressing question - what are those things around their cocks?
Is the festival organized for them or just for the tourists?
The reason most people go there is to attend an annual festival. It's sort of like a sports event in the West - organized for viewing pleasure of the fans but thoroughly enjoyed by the participants as well. The feeling I got is that it's a way for these guys to reenact their traditions / history, which would otherwise wither away.
How advanced was their society before encountering civilization?
They were settled and had mastered agriculture (sweet potatoes, pigs). They were living in villages - men in one house, women and children in another. Men had multiple wives (was kinda needed as they stopped having sex for 5 years after birth of a child).
Culture-wise they were pretty primitive. The villages were in a constant state of war. War may be too strong a word for it - more like low-intensity conflict (raiding parties for women / pigs, ambushing each other, etc). It basically gave men something to do - as otherwise their needs were fully met and they didn't have much culture or religion (they worshipped ancestors, etc). They did practice cannibalism - you'd cut out a body part of an enemy that you killed and eat it to gain their strength. They also had the habit of chopping off women fingers as a form of sacrifice - if a woman's husband died, that's what would be done to her.
What political entity are they part of today?
The entire Papua Island was split in two - Western part was part of the Dutch New Indies and the East was Portugese. Japanese have occupied the island during WW2 and after they were thrown out by the Americans, Indonesia proclaimed independence in 1945 (on Aug 17th). Papua was going to be an independent country administered by the Dutch until they could have self-governance (as majority of the population at the time was literally beyond illiterate).
The Western Part of the island became an independent nation Papua New Guinea. The Eastern part was taken over by Indonesia in 1960s (kinda like Tibet and China). Even though the UN was set on granting them a status of independent nation (they have absolutely nothing in common with Indonesia other than being both ruled by the Dutch for 300 years) - Cold War politics intervened and the US supported Indonesia in the takeover (fearing that they'd switch to the USSR otherwise).
Since then a low-level war has been going on - Papua Conflict. Indonesia doesn't want to let the province go (it's fairly rich in natural resources) and is moving millions of "real" Indonesians (ie people from Java) to the island (so now half the population is not Papuan). The Papuas don't want to be ruled by what they consider an occupying colonizer. It's a situation very similar to Tibet but with lower stakes (as these guys never had a political entity and nobody outside the area even being aware of the issue).
Are they black (ie African)?
No, they are not. They are a disctinct group of people who are closely tied to Melanesiand and Australian Aboriginals: https://en.wikipedia.org/wiki/Papuan_people
In the photos they may look African as they cover themsleves with some kind of soot (perhaps war paint).
Should I go there myself?
That's a personal question. Overall the trip is long (it takes almost a full day of flights from Bali / Jakarta) and the conditions there are very, very basic. However it's a fairly unique place that's unlike any other.
If you really do make the visit, I'd recommend getting in touch with local guides to see if you can fly a plane to visit the real remote tribes (ie people who are still living in the stone age now).