Hi
OP, welcome to Dakka, try not to be put off by some of the more over-zealous posters
The best advice is to firstly check what your local players use in terms of restrictions.
GW have some suggested restrictions on the number of detachments and number of duplicates of the same unit you can use in an army (generally 3 detachments and 3 of any one unit) and if these are in use you may have some issues trying to put together a 4-god Daemon army. You get bonuses if a detachment only contains units dedicated to one god (so all Slaanesh units or all Khorne, for example). You can mix units form different gods in a single detachment but you'd lose those bonuses. SO if you want to take an army representing all 4 gods you'd either need 4 detachments (which may not work if your local groups use the 3 detachment limit) or you need to lose some bonuses by mixing units from some gods in one or more detachments.
So it's possible, but potentially tricky and not very powerful. More feasible is trying to do an army for 2-3 different gods. If your local groups aren't too competitive, you may well be fine building an army of all 4 gods, either because they don't use the suggested restrictions or they're not using powerful lists so losing a bit of power by running all 4 gods in one detachment may not be too much of a drawback.