How should my strategy change in an MTG Draft based on the number of players?
The traditional number is, of course, 8 players. This is the only pod size used in high-level tournaments as far as I know, but for something more casual like FNM, it's not uncommon to hold drafts with 6 to 10 players. Personally I've participated in (non-sanctioned) drafts with 4 players and with 9 players.

Perhaps surprisingly, the difference in the size of the card pool isn't that significant. Keep in mind that even though you'll have fewer (or more) cards to choose from, there are also fewer (or more) people to choose them. As long as you draft with 3 packs (42 or 45 cards) per person, those two effects balance each other out. It is an imperfect balance, though. Your decks tend to be a bit looser in a smaller pod, in the sense that if you're drafting a very specific archetype (perhaps one that relies on a specific card), you probably won't see enough of the cards that archetype needs to build the deck as focused as you would in an 8-player draft. You'll have to branch out and incorporate some cards that are less relevant to the deck you're trying to build, or perhaps combine two or more specific archetypes. Taking Innistrad draft as an example, instead of drafting a self-mill recursion deck as you might in an 8-player pod, if you're in a 4-player pod you might have to draft blue fatties, only some of which will be relevant to the recursion theme. Inexperienced drafters tend to just draft broad color-based strategies anyway, so they will likely not be affected much by the change in the pod size.

A much more noticeable difference, in my opinion, is that as the pod size shrinks, there are fewer people intervening between your first and second picks from a given pack, and so your chances of tabling your second or third choice card from the pack goes way up. As long as your archetype of choice is sufficiently broad, it's actually easier to make a consistent deck in a small draft pod. If you think about it, with 5 colors and 4 or 5 players, there's a decent chance that the colors will sort themselves out 1 per player.

Conversely, as the pod size grows, your chances of tabling any given card in a pack goes down. In fact, if you go up to 9 drafters, there will be 3 whole packs which you only see once. With 10 drafters, there will be 5 packs you only see once, and so on. This phenomenon reduces your ability to communicate with the rest of the table through your picks, and so you're less likely to get cards that fit into your strategy late in the draft. You should still be able to make a fairly focused deck because of the large card pool, but be prepared to have to fit in some "stragglers," cards that you wouldn't ordinarily want in your deck. 

I've heard a lot of people say that pods with an odd number of drafters (like 7 or 9) are undesirable. I'm not sure why that is, though. The effects I've discussed above are minimal for a 7-person or 9-person pod, so the only disadvantage I can think of is that one person has to sit out each round during the games.