Yes, the Orthodox Church has kept some of the Judiac traditions. I am not the best qualified
at all to answer this, but I thought I'd try to give you
something, since we have a lot of Saturday sleepy-head slackers around here......
Anyway, I just know that someone has a link to great information on this......but I'll relate what little bit I know.
1. Orthodox acknowledge that sabbath begins sundown on Fri., just as the jews did. However, we believe Christ is the fulfillment of the sabbath, as He is the fulfullfment of all things in the OT. So, we worship on Sunday in acknowledgement of Christ's glorious resurrection. We do also have a Sat. eve prayer service called Vespers.
2. We observe Passover in a sense, only we call it Pascha. Again, since Christ is the fulfillment of the Passover Lamb, and He has freed us from sin (instead of just Egypt in OT). So we celebrate His death and resurrection at Pascha (Easter), which ir preceeded by 40 days of strict fasting and prayer (Great Lent).
3. We do fast twice a week as the jews used to (not sure if they still do), but we fast on different days (W/FR).
I think there are other feasts that have Judaic roots, but I'm too much of a newbie to the faith to tell you about them. If I am inaccurate on anything, someone please jump in and correct me! I'll do some snooping around to see if I can find links to things