Edit: I’ve thought about this more and realized that it’s not as complicated as it seemed.
The object pronouns for the imperative are mostly the same as the ones you usually use for verbs; moi and toi are the only exceptions.
Chart & examples
Here are the object pronouns when used in the imperative:
Here are some examples of the imperative pronouns in action:
Dites-moi ce que vous voudriez. ← dire à moi
Montre-lui ta solution. ← montrer à lui
Parlons-leur de ce problème. ← parler à eux
C’est ton anniversaire. Fête-le ! ← fêter l’anniversaire
Ces biscuits sont-ils les vôtres ? Mangez-les donc ! ← manger les biscuits
Les informations qu’elles ont demandées ? Donne-les–leur. ← donner les informations à elles
Why would this be?
I find that these pronouns are best viewed as separate systems with a lot of overlap. When comparing that chart with this one, you’ll see that all the pronouns cross rows (used for multiple persons) and columns (used in multiple scenarios). There’s no hard-and-fast rule to predict which form a pronoun will take anywhere; you just have to know these charts.
However, Gilles’ comment and answer suggest that this has to do with the position of the pronoun. If it comes before the verb, we use the weak form: me and te. But if it comes after the verb, we use the strong form.
We can test this to some degree using the negative imperative. The negative imperative generally has the pronoun before the verb. Sure enough, we get the normal object pronouns:
Ne me dites pas ce que vous voudriez. ← dire à moi
Ne t‘en fais pas. ← faire à toi-même
But there’s a colloquial version where you can put it after, and here it becomes the "strong" version:
Fais-toi-en pas. ← faire à toi-même (Daniel Lavoie, « Ça c’est ça »)
So the theory works — but hang on, which system is it that gives us the "strong" version?
- If we say it’s the tonique, we have to explain why we use lui instead of elle.
- If we say it’s the COI, we have to explain why we use moi and toi instead of me and te.
- Maybe it’s the COI in general, but since me and te are weak forms, the tonique replaces them.
In any case, you can see my point: somewhere it becomes hard to explain why this or that system is used in a specific scenario,1 and you more or less have to just view it as a chart to memorize. That’s why I made the hopefully handy ones above. 🙂
1 Without diving into historical linguistics to trace all the stages of each pronoun.
This is not about the verb, it’s about the pronouns. The first and second person object pronouns moi and toi have different forms when they are placed before the verb: me and te. Normally, for a direct complement (COD) or an indirect complement (COI) introduced by à, the pronoun form is me/te placed before the verb. But in an imperative sentence, the verb has to come first; this rule is stronger than the rule about pronoun placement. So the pronoun moves just after the verb, and there’s a hyphen between the verb and the pronoun as a sort of reminder that the pronoun is more closely attached to the verb than it normally is. Furthermore, the forms me and te cannot be used after a verb, so they change back to moi and toi.
The rule about the placement of the pronoun applies to all persons, not just first and second singular, but for other persons the form of the pronoun does not change. In particular, the third person forms are e.g. donne-lui and donne-leur even when they are feminine: lui does not change to elle in this case.
I think the simplest way to explain it is that the weak pronouns in general tend to have a different form depending on whether they come before or after the verb.
Here’s a chart (with the IPA transcription to show some phenomenons the orthography hides) showing the change in pronouns depending on their placement relative to the verbal stem:
What I hope this indigest chart makes clear is that almost every weak pronoun behaves or is pronounced differently depending on whether it appears before or after the verb, except lui and leur. But for most of them, French’s orthography camouflages it, often by marking the change on the verb instead (Mangé-je, Vas-y).
There’s a few exception to this principle, mostly in that in the formal language the combination of post verbal me/te and y/en gives -m’en/-t’en/-m’y/-t’y (i.e. the preverbal forms), but quite conveniently Colloquial French regularises them away to moi-z-en, toi-z-y and so on.