Is saying "by men," "by manhood," or "by 'al-tirs'" when asking for something, and saying "I seek your protection, do such and such" or "I seek your protection, give me," considered swearing by other than Allah?

The apparent meaning of the phrase "I ask you by God and by your honor (or, I seek your protection)" is that it falls under the category of seeking intercession with others to fulfill a need, which is permissible. And "by your honor (or, I seek your protection)" is not an oath by other than God, but rather it intends a plea.