The verse does not actually say that "the Jews will be oppressed for 400 years." Rather, it says that they will be strangers in a foreign land, and they will be oppressed and enslaved, for 400 years. The verse is listing three stages of increased difficulty -- first, being strangers in a foreign land; second, suffering oppression ("Inuy"); and third, suffering slavery ("Avdus"). From the beginning of these three stages until the end, there are four hundred years. See MALBIM who expounds on this, and YALKUT SHIMONI 1:77 who alludes to it. (See also RAMBAN and others who offer other approaches to your question.)

Y. Shaw