Weird sorting algorithm

Since you're only processing so few elements, you could just fit the whole list into an array, then sort it with qsort. Here's a quick example. Be careful not to overflow the nodes array in print_sorted - for such few nodes, you could just go through the linked list once to get the size, then malloc the space you need.

Notice that in the example, node_compare works with an array of pointers to node. If you want to work directly with an array of nodes, just remove the dereferences at the start of the function and cast them to const struct node * instead of const struct node **.

// for qsort
#include <stdlib.h>
// for strcmp
#include <string.h>

struct node {
    int data;
    char word[125];
    struct node* next;
};

int node_compare(const void *a, const void *b) {
    const struct node *first = *(const struct node **) a;
    const struct node *second = *(const struct node **) b;

    // Order nodes with same data alphabetically
    if (first->data == second->data) {
        return strcmp(first->word, second->word);
    } else {
        return first->data - second->data;
    }
}

void print_sorted(struct node *list) {
    struct node *nodes[512];

    // gather whole list into the array
    struct node *current = list;
    int arrayIndex = 0;
    while (current != NULL) {
        nodes[arrayIndex++] = current;
        current = current->next;
    }

    // sort the array
    qsort(nodes, arrayIndex, sizeof(struct node *), node_compare);

    // print em
    for (int i = 0; i < arrayIndex; i++) {
        printf("data: %d, word: %s\n", nodes[i]->data, nodes[i]->word);
    }
}

int main() {
    struct node a = { .data = 3, .word = "ayy", .next = NULL };
    struct node b = { .data = 3, .word = "zzz", .next = &a };
    struct node c = { .data = 3, .word = "ddd", .next = &b };
    struct node d = { .data = 10, .word = "toaster", .next = &c };
    struct node e = { .data = 0, .word = "box", .next = &d };

    print_sorted(&e);
    return 0;
}

This prints out:

data: 0, word: box
data: 3, word: ayy
data: 3, word: ddd
data: 3, word: zzz
data: 10, word: toaster

If you want descending order, change the bottom part of node_compare() to the following:

if (first->data == second->data) {
    return strcmp(second->word, first->word);
} else {
    return second->data - first->data;
}