There's a popular fan-made format called Cube where you create a set of cards and people pick them for their decks, either by assembling virtual "packs" by grabbing random sets of cards or (more rarely) picking them one-at-a-time from the whole set kinda like how teams draft rookie players in professional sports. Because you tailor the card pool to your group's needs, it's easy to create Cubes for unconventional formats like Commander (individual collection permitting).
If you're interested in having pack-based drafts that strongly resemble normal MTG Limited and Sealed, you can assemble your own packs from your personal collection, basically like Cube draft but with rarity. Here's a rough guide...
To my knowledge, the only thing that's truly fixed about boosters is rarity distribution (although you can get extra rares in a pack due to foils, or specialty stuff like double-faced cards or "hidden treasures"). There are some other correlations that arise due to how sheets are cut, but they're mostly at the box level rather than individual-pack level.
If you start with a fairly representative sample of a set and then construct cards with the same rarity distribution as regular MTG boosters, the laws of probability should ensure that you get a reasonable distribution of colors and card types in the vast majority of your packs (a few really skewed ones is acceptable or even desirable, just like you sometimes get really skewed "official" boosters). The easiest way to do this is just to create three big piles for commons, uncommons, and rares (/mythics) and make packs from them sight-unseen in the normal 1:3:10 ratio; you don't have to do anything special for the individual packs as long as your starting piles are at fair (e.g. if you collect certain colors much more heavily than others, make sure that bias doesn't filter into the big giant piles you've created). Ideally your big piles should be significantly bigger than the number of cards in any given draft; that way there's no guarantee that a particular card is bound to be in one of the packs.
The easiest way to create a coherent environment is to stay within a given block (set of 3-4 expansions). Playing a familiar block format will make it easier for players to evaluate cards. I don't think the extra effort that would be required to make sure your packs exactly match individual sets (like they do in "real" Limited) is really worthwhile -- if anything, I think you can have a more fun block draft if cards from the various expansions are mixed together across all three packs.
Of course, you can also vary (or just abolish) the rarity mix in order to create a very different play experience. I'm assuming other ways to alter the experience will come to you once you've tried this a few times. If you find yourselves wanting to fine-tune what goes into your card pool, look for articles on Cube drafting: the same principles folks apply to creating a Cube can be used to analyze what you're putting into the pool you draw packs from.