Depends on the spells point of origin
Wall of Force states:
An invisible wall of force springs into existence at a point you choose within range. (...)
Nothing can physically pass through the wall.
Most spells need a line of effect to their target, and therefore Wall of Force blocks nearly every spell. The question if Moonbeam can be cast through a wall of force has already been marked as a duplicate of the question about casting spells through it.
In your case the spells are already cast prior to the wall. There is nothing in the text of Wall of Force that says it would negate an existing effect already in place, but the effect needs to still have unblocked lines from the point of origin, because of the rules for area of effect:
A spell's effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn't included in the spell's area. To block one of these imaginary lines, an obstruction must provide total cover. (p. 204 PHB).
Light can pass through the wall, because it is described as invisible, and Moonbeam creates light. Does that matter? No. It has been established that Light from Wall of Light has its effect blocked due to the area of effect rules.
The light from Moonbeam likewise originates from a point at the top of the cylinder, as the spell describes the light shining down, and the point of origin for a cylinder is on its flat end (PHB, p. 204). So the effect of the moonbeam light would be blocked.
Stinking cloud has a sphere as area of effect. The point of origin is in its center. If you put the center close enough to the floor, then the point of origin would we within the dome created by Wall of Force, and the effect would persist within the walled area (but not outside of it any more)
Controlling Flaming Sphere
The PHB does not explicitly say anything about needing line of effect for controlling the sphere. As other effects that do not need line of effect like teleportation can pass a Wall of Force, I think you could move the sphere, but it is not unequivocal. This may be an area for adjucation by your DM (thanks to ExemptMedic: more discussion on this).
Is the rule for area of effect only checked during the casting of the spell, or continuously later on? The text in the PHB does not limit it to the time of casting explicitly. Existing precedent answers like that for Wall of Light indicate that it is checked continuously, and this answer assumes this to be the case.
For some spells with a persistent area of effect this does not matter, as the spell explicitly states what happens if a barrier is introduced (darkness, or daylight), or that the effect emanates from a certain point or direction (moonbeam, gust of wind).
For others, like entangle, or your example of stinking cloud, the spell has no such statement, and the effects of applying continuous checking seem somewhat counterintuitive -- why would the gas that already was created vanish if you place a wall through it?
There also is some weak support that the PHB does not consider ongoing area of effect spells when discussing area of effect, because both examples cited (burning hands and cone of cold) are instantaneous, and it would have been easy to replace one of them with an example like stinking cloud.
The section of this answer about stinking cloud would change if line of effect was only checked during casting. In that case, the gas on either side of the wall would persist. You would not need to place the point of origin inside the dome to affect creatures in the dome.
There are arguments for either treatment, so I think until we get Sage Advice clarification, these edge cases will need adjucation by your DM.