Learn English – What does this mean: ‘Chuck Norris can lead a horse to water AND make it drink’? Why is it funny

Although the phrase can mean that, and often does, it's also sometimes applied in a more broad context. To be "swept off your feet" is to be surprised, enthralled, exhilarated. Critics can be swept off their feet by an epic film; operagoers can be swept off their feet by a beautiful aria, etc.

As for how sweeping became associated with love, that's referring to the aspect of sweeping that means a smooth movement, not the act of using a broom. Ballroom dancers can sweep across the dance floor, a powdery snow can sweep across the barren fields. It's that smooth, fluid motion – and the idea of your emotions being carried in that fashion – that brought about the idiom. A strong ocean or river current can literally sweep you off your feet, and young lovers can do the same thing to each other, figuratively and emotionally.

In my opinion, the adverb enough used in this sense creates a conversational rapport between the speaker/writer and listener/reader. In strangely enough, interestingly enough etc., the enough might mean "enough to go so far as to consider it such". The reason it's used is perhaps a fear that the addressee might not feel the described circumstances really warrant the qualification strangely/interestingly/etc. By using it, the speaker/writer acknowledges that their listener/reader is right to think that, but that the circumstances really can be considered such for the sake of their conversation.

In any case, this enough is not used in a formal register. When it is used in a formal setting, it signals a (temporary) lowering of the register.

Just my two cents.