MergeSort k arbitrary words in linear time
General case:

If there is a linear time sorting algorithm $\mathcal{A}$ for this problem, then one can divide a list into random parts, and use $\mathcal{A}$ to sort. But comparison based sorting has a lower bound $\Omega(n \log n)$. Therefore there is no such algorithm $\mathcal{A}$.

Note: Merge routine combines sorted arrays into one sorted array. There is a similar problem to your problem called k-way merging, but that is also required sorted arrays. The complexity of k-way is $\mathcal{O}(n \log k)$

Finite alphabet case:

If we assume that the alphabet is finite, and in your case it seems only lower case letters then one can use the Counting Sort algorithm.

Assuming that the total length of the words is $n$ and there are at most $t=26$ letters, the Counting sort can sort this array in $\mathcal{O}(n+t)$-time.

To achieve this with Counting sort, you need to convert this into an array and map the letters with an integer. And, call;

 countingSort(array,26)


The Counting sort is not in-place. The space requirement for this question is $\mathcal{O}(t)$


Note 1: Counting sort is not a comparison based sorting algorithm, it uses counting, thus it is not bounded by the lower bound of the comparison based sorting algorithms.
Note 2: Counting sort, also, can be implemented stable.