For the first question, just looking at Strong's numbers introduces the conflict here. The Greek words all come from the same word but are different forms of that word. Strong's numbers combine all forms of a word. That number is what you look up in a lexicon containing Strong's codes.
English is not a highly inflected language. That means that we rely on word order to show meaning. Greek spells words differently to show if they are the subject or object of the sentence.
10:38 Ἐν δὲ τῷ πορεύεσθαι αὐτοὺς, αὐτὸς εἰσῆλθεν εἰς κώμην τινά· γυνὴ δέ τις ὀνόματι Μάρθα ὑπεδέξατο αὐτόν.
10:38 Now as they went on their way, [he] entered a certain village where a woman named Martha welcomed him as a guest. [I replaced the NET's Jesus with "he" to keep the pronoun]
- αὐτὸς - This is the root or lexical form. Pronounce it as "autos" with a short o sound. It is the 3rd singular, masculine, nominative pronoun (often abbreviated 3SMN or NM3S).
- αὐτοὺς - Pronounce it as "autous". This is the 3rd plural, masculine, accusative form (3PMA or AM3P).
- αὐτόν - Pronounce it as "auton" with a short o sound. This is the 3rd singular, masculine, accusative form (3SMA or AM3S).
The first in the bullet list is the nominative case. It serves as the subject of the verb. "He entered."
The two accusatives receive the action of the verb. The last is simpler to explain. Who did she welcome? Martha welcomed "him."
In the first sentence, the verb itself is plural and shows that more than one person is making the journey. But αὐτοὺς is accusative and not nominative. αὐτοὺς receives the action. Were it to merely emphasize, αὐτοἱ would have been used. This is why the NIV has "they were on their way." The pronoun and case doesn't transfer to English on a one-to-one basis.
For the second question, why did the NIV use "and the disciples" in place of "they," this was a decision made for clarification. Who is "they"? Jesus and the disciples. Since a new paragraph was starting, they wanted to be clear on who "they" were (the subject was contained in the plural verb). The NET Bible made a similar decision when they left "they" in the first clause but changed the "he" to "Jesus" in the second.