I would like to knock out part of a wall in my kitchen to recess my refrigerator, so I knocked out the drywall on the other side of the kitchen wall .This was approx. 30"x65". In this space are 2x4's, how do I tell if they are supporting? Can I just knock them out? I have a 1941 cottage. The 2x4's are right below what looks like a center support beam in the kitchen.Can they be moved? Help!:)

Could very well be in the description you gave. Can't tell for sure without more information. However, you should have someone who is qualified to come and look. You cannot knock down walls without knowing. This is not a "simple" do it yourself ordeal. All weight/structual support walls cannot be removed without adding support, then adding a header for that required area. At all times this area is supported by a temporary wall, while the support/head etc is being done.

Do not remove any studs or any supports in any way until you have a very experienced contractor there to help you.
NOT someone who thinks they know, but do not know. The last time this happened, I went to the home and this had already been done. The house had to be condemned. He had not consulted with enough knowledge, only someone who "thought they knew enough".

Sorry for that run on...
Now that I have said that, it would help to see the location. A small area that is NOT wieght bearing, can be done easier.

Do not remove wall if beam rests on top of it. In which case, to remove that wall you have to cut one small section of the wall and brace very well before you remove the rest and then, you would need a permanent support column or several colums depending on the span of the wall.