Contradictory meanings within a single root is fairly common occurrence amongst Semitic languages. The phenomenon repeats itself consistently in Arabic and Aramaic, so there's no reason why it wouldn't be the case here.
1) Jastrow's dictionary has all three definitions listed, although he lists Hilutz earlier. According to him, the definition of "strengthening or girding one's self" only occurs in Hif'il, Pi'el and Pa'al.
2) I'm not sure what the Alkalai Hebrew Dictionary says, but since it's one of the most authoritative, I wouldn't be surprised if it gives both definitions. The Modern Hebrew dictionaries I looked at all give the definition of "removing" rather than that of "strength" or "girding yourself with weapons". If someone could verify that, that would be great.
3) There is no direct cognate in Arabic, although a similar sounding root, Khalasa, retains both meanings in verb forms 10 and 2.
Based on this, it seems that both definitions are acceptable, although the one of "girding one' self" is less common. The alternative is a ugly borrowing situation that I don't believe to be possible in which either the Aramaic (if there is a similar word) or Arabic word was incorporated into Hebrew and later on the confusion of /Kh/ and /h/ lead to the words being merged into one.