Let's start at the beginning, the 6 principal parts:
  1. Present Tense:
    If we know this form we know
    whether it is an -ω verb or
    whether it is na -μι verb.
    and can now form all the other present tense forms:
    • present indicative
    • imperfect
    • imperative
    • present subjunctive
    • present optative
    • present participle
    • infinitive
  2. Future Tense
    Knowing this form will gve us the future stem, which, together with the -ω verb present tense endings will form the
    • future indicative
    • future optative
    • future participle
    • future infinitive
  3. Aorist Active/Middle.
    Just like in the Present Tense where we have 2 sets of endings according to whether we are in the presence of a 1st person present tense form in -ω or in -μι, in the Aorist we have 3 different sets of endings according to the form we find here:
    • a form ending in -α usually called 1st aorist. And, as most things 1st, its stem is not too difficult to work out, if you know the present tense 1st primitive part.
    • a form ending in -ον (active) or -όμην (middle), usually called 2nd aorist. It has a different stem that has to be learnt because it can't be worked out by looking at primitive part #1. Except very rarely (-άνω verbs e.g.: μανθάνω, λανθάνω, τυγχάνω..... To compensate, their other forms are easy: same endings as in the Present Tense.
    • a form ending in -αν, -ην, -υν or -ων. I don't know why this form should be called aorist of -mi verbs since the only -mi verb that follows the pattern consistently is ἵσταμαι, στήσομαι, ἔστην,..... I stop, will stop, stopped (myself, stood still).
      The only thing this aorist has in common with present tense -mi verbs is this: the endings are added directly onto the stem vowel, i.e. they are athematic. So calling this aorist "athematic aorist" is much more appropriate.
      The forms of this "athematice" aorist follow the same pattern as primitive part #6 aorist passive, another athematic aorist, passive in meaning though active in form.
      To my mind calling this form 2nd aorist of -mi verbs doesn't make much sense, because most -μι verbs are straightforward 1st (or 2nd, mostly intransive and middle) aorist, conjugated exactly like the 1st (or 2nd) aorist of -ω verbs. For an example of a -mi verb using both aorists, see ἀπ-όλλυμι, ἀπολῶ, ἀπώλεσα(transitive) andἀπωλόμην (intransitive)
      Except of course for the trio δίδωμι, δώσω, ἔδωκα
      Except of course for the trio τίθημι, θήσω, ἔθηκα
      Except of course for the trio ἱημι, ἡσω, ἧκα
      But these 3 couldn't make up their mind: 2 different stems and 1st aorist endings -α, -ας, -ε for I, you, he/she/it but 2nd aorist endings, slightly modified, for the rest of the aorist indicative, imperative and infinitive, both active and middle.
      Their other modes (subjunctive and aorist), and their participles do follow the so-called aorist of -mi verbs pattern.
There are actually 4 aorists:
1. 1st aorist, like 1st declension (Latin or Greek), 1st conjugation (Latin) has endings in -a (since a is the first letter in the alphabet it stands to reason to call a-conjugations 1st
2. 2nd aorist (both active and middle) with both (unpredictable) stem change and a different set of endings
3. passive aorist (mostly passive in meaning but active in form) which again, like principal part #3 (active/middle aorist) has 2 sub-sections:
a. the -θην variety [ἐβουλήθην and (koine) ἀποκρίθην are active in meaning]
b. the -ην, -ων and -αν variety (stem change, no theta, but endings perfectly consistent with the -θην variety. [this group includes quite a few active meanings]
 
The 2nd aorist of ὄλλυμι is a real 2nd aorist (principal part #3) and therefore has principal part #3 2nd aorist [middle] endings: -ομην, -ου, -ετο, -ομεθα, -εσθε, -οντο