You're going to have to do some work to figure this out.
I see three cables coming into the box. One of those is the 'feed'. The feed should be whatever is 'hot' if the power is on to the box. You need to find that first and isolate it so you can work safely- cap them. off.
You also said one of the white wires is 'hot'. That's usually only done when making a 'runner', aka a wire that heads to a three-way switch (two or 3 switches can turn on a light). If you ONLY have a white wire as 'hot' when the circuit breaker is on, please stop, as that IS NOT NORMAL. Either way, said white wire SHOULD have a black marker or electrical tape around it to designate 'runner'. It's possible that an earlier wire downstream was flipped around accidentally and you've energized the neutral by accident.
Once you find the hot/neutral pair for the main circuit, the switch needs 2 wires out- hot and runner, the second switch (if it's a single) needs just a single line out, and the outlet needs a hot and neutral.
The outlet will be piggybacked to feed the two switches, most likely. You'll also need to piggy the neutral to the return from the lights so the circuit can be completed.
I know this sounds complicated but it's really important to know what wires are what- and if you aren't comfortable with that or don't have the tools, you need to hire an electrician or find someone that does- especially since you've said a white wire was hot.