Without cheating, I was only able to get three of them (the Greek god, the terrorist organization, and the board game). I got the answers to three more, but I had to look up lists of Beatles songs, British PM's, tribes of Israel before I realized that I already had them. I was able to get the bird by just writing down all the things I came up with that sounded like they might be words and searching for them on Wikipedia. I have no idea about the mammal. Here are some hints:
The names of Greek god, the Beatles song, and the board game are all also common words.
The names of the British prime minister and the tribe of Israel are also well-known proper nouns for other reasons.
The name of the terrorist organization has the emphasis on the last syllable, but the nation name it's derived from has the emphasis on the second-to-last syllable.
The name of the bird is very short and you may not have heard of it before.
Of course, the first nation I tried this game on yielded absolutely nothing. After I was doing it for a while, I found a nation that yielded many layers. Eventually I ended up looking at a sticky mess, and I discovered I had a bit of an obsession. But finally, I was able to find a friend.