I don't understand why sometimes the article is not necessary. btw "entra nella macchina" should be aceptable?
There isn t the article because it wants to give a stronger meaning to the affermation.
Can I say "enter the vehicle" or is vehicle an entirely different word?
No it's the contrary. "(Lei) entri" is the subjunctive present, 3rd person singular, form of "entrare". The subjunctive is also used to express a prayer, a kind order. Here, the prayer, or the kind order, it depends on the context, are expressed in a formal way thanks to the 3rd person singular, which is the formal you (Lei). If you say "Entra in macchina!", you're using an imperative (which has only the present tense), 2nd person singular. The imperative expresses a strong order, a constriction, like the English one. So it is ruder than the subjunctive. It is even ruder thanks to the use of the 2nd person singular (tu), which is the informal you. Hope to have been clear. Cheers!
Sorry, now I have re-read your sentence and I realized that entri is also the present indicative, 2nd person singular, of "entrare". Intended in this way, "entri" is used to make questions. E.g.: Entri in macchina? (Context: an annoyed boy to his friend who is doing something outside the car while the air conditioner is on). However, the indicative is used neither to express an invitation, rude or kind, nor a constriction.
Lorendani, an interesting take I haven't come across before. Lei , entri is the formal command (imperative) . The tu form, entra is just that, the informal command. It is not rude, just informal although I imagine it may be seen as such if you are using it to a person you should be speaking formally. Entri as you correctly said is also the subjunctive which is not a tense but a mood and is used wherever there is doubt or uncertainty and after certain adverbs. Although it looks the same, it is not the imperative and shouldnt be confused with it, I have never heard of it described as a prayer or king of order. It has its own rules. Erikvan, entra =informal imperative, entri= formal imperative Subjunctive=a whole new world of fun