"Ich gehe ans Telefon" (short and slightly colloquial: "Ich gehe ran") or "Ich nehme den Hörer ab". The latter refers to times when you had to lift the receiver from the base of a phone and is still sometimes (seldom imo) used in the short form of "Ich nehme ab".

Abnehmen has the more common use of saying "I am loosing weight". As AHA said, in your usage it was about lifting the receiver of a phone landline. In times of cellphones its usage may disappear sometimes soon.

Nothing, but abnehmen is a bit more formal.