Step 1: Understanding the Concept
Immunity may be natural or artificial, and active or passive.
Step 2: Statement (I)
A vaccine deliberately gives antigens, so the immunity is artificially acquired active immunity, not natural. Statement (I) is incorrect.
Step 3: Statement (II)
Oral vaccines (such as oral polio) have long been in use. The latest focus is on DNA and edible vaccines. Statement (II) is incorrect.
Step 4: Conclusion
Both statements are incorrect.
Final Answer:
Both Statement (I) and Statement (II) are incorrect.
\[ \boxed{\text{(B) }\text{Both Statement (I) and Statement (II) are incorrect.}} \]