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外来語 is neutral and can be used both in formal and informal language. In a narrow sense, 外来語 excludes the Chinese vocabulary and its derivatives, but sometimes it includes loan words from Asian languages. Technical terms are often regarded as jargon, not 外来語, unless they are part of daily vocabulary.
カタカナ語 sounds slightly informal and sometimes carries a negative connotation. Obviously it excludes loan words in Kanji such as Chinese words. The negative sense stems from the fact that they don't exploit the ideographic feature of Japanese and that many カタカナ語 has already synonyms in kanji in the first place, i.e., it may imply "Don't fuck up Japanese, you faggot."
横文字 includes all kinds of imported word from Western countries. Not only does it include カタカナ語 or 外来語 from European languages, but you can refer to, say, English words in Latin alphabets in Japanese text. The Japanese words in my post are opposite to 横文字 in the sense that they are written in kana and kanji and mixed in an English post. Sometimes 横文字 carries a negative connotation for the same reason as カタカナ語.