搬出 and 搬出去 share the meaning of "moving out" in general. While there are some differences between them.
1 搬出+Object. this object represents the original place. eg. 他搬出他女朋友家，因为他们分手了。 He moved out from his girl friend's place, because they broke up.
In this case, using 搬出去 is not correct.
2 搬出去+（到）+Object. this object represents more the destination place. eg. 他搬出去到他哥哥家。 He moved out and moved to his elder brother's place.
3 In oral expression, if only wanted to mention "move out" as an order.Saying “搬出去！！” is correct and enough while if you only said "搬出！“, I guess the audience would laugh. :D
4 搬出+O. means provide out, take out. While "搬出去" doesnt have such meaning. In this case, this object is more abstractly stuff. such as reason, excuse, explanation etc. For example, 每次他迟到，他总是搬出一大堆借口。 He always provide a lot of excuses when he is late.
Hope this answer helps you. ;)