Step 1: Understand the question.
The question asks to identify the specific plants that store water in the form of mucilage in their root, stem, and leaves, respectively. This implies a sequential order of plant parts for water storage in mucilage form.
Step 2: Analyze the characteristics of the plants mentioned in the options regarding mucilage storage.
\begin{itemize}
\item Asparagus (root): Some species of Asparagus, particularly those adapted to dry conditions, develop fleshy roots that store water and nutrients, sometimes in the form of mucilage.
\item Opuntia (stem): Opuntia (prickly pear cactus) is well-known for its succulent stems (cladodes) which are highly adapted for water storage, primarily in the form of mucilage to conserve water in arid environments.
\item Aloe (leaves): Aloe vera and other Aloe species are famous for their thick, fleshy leaves that contain a gel-like substance rich in mucilage, serving as a significant water reservoir.
\end{itemize}
Step 3: Evaluate the options based on the observed water storage mechanisms.
\begin{itemize}
\item Option 1: Asparagus, Opuntia and Aloe - This option correctly aligns Asparagus with root storage, Opuntia with stem storage, and Aloe with leaf storage of mucilage.
\item Option 2: Opuntia, Aloe and Casuarina - While Opuntia and Aloe store water, Casuarina (she-oak) is typically a xerophytic tree that reduces water loss through modified stems/leaves, but not primarily through mucilage storage in the way described.
\item Option 3: Opuntia, Calotropis and Aloe - Calotropis (milkweed) is a xerophyte but does not store water in mucilage in its leaves in the same prominent way as Aloe; its stems contain milky latex.
\item Option 4: Asparagus, Aloe and Calotropis - This option mismatches Aloe with stem storage and Calotropis is generally not known for mucilage storage in leaves.
\end{itemize}
Step 4: Conclude based on the evaluation.
The combination of Asparagus for root, Opuntia for stem, and Aloe for leaves accurately represents plants storing water as mucilage in the specified parts.
The final answer is $\boxed{\text{Asparagus, Opuntia and Aloe}}$.