Step 1:
Lingaraja Temple and Jagannatha Temple are famous temples located in Odisha.
Step 2:
Pashupatinatha is in Nepal, Kamakhya is in Assam, and Vaidyanatha is in Jharkhand/Bihar region.
Step 3:
Only D and E belong to Odisha.
Step 4:
Hence, the correct answer is:
\[
\boxed{\text{(1) D and E Only}}
\]