If I am prior service Army looking to go to the Navy Reserve, can I wear US Army awards and badges on the Navy working or dress uniforms?

Refer to the Navy's uniform regulation (NAVPERS 15665J)* for detailed answers.

For awards, the answer is generally yes, but for most badges/tabs/etc., other than marksmanship badges, the answer will be no.
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* U.S. Navy Uniform Regulations (NAVPERS 15665J), Chapter 5 - https://www.mynavyhr.navy.mil/References/US-Navy-Uniforms/Uniform-Regulations/Chapter-5

Short answer is yes but for specifics you need to look at the order and look at the specifics. Col Cudworth already pointed you in the right direction.

Most U.S. military awards (ribbons or medals) can be worn when transferring from one branch to another, badges not necessarily the case. COL Randall C. has given you the best place to look and find out what is authorized.