Any spell of 5th level or lower cast from outside the barrier can't affect creatures or objects within it, even if the spell is cast using a higher level spell slot. Such a spell can target creatures and objects within the barrier, but the spell has no effect on them. Similarly, the area within the barrier is excluded from the areas affected by such spells.
There is an ambiguity here.
Similarly, the area within the barrier is excluded from the areas affected by such spells.
What is "such spells"?
"such spells" could be "Any spell of 5th level or lower cast from outside the barrier", or it could be "Any spell of 5th level or lower cast from outside the barrier" that "target creatures or objects within the barrier".
I'd argue this is a weak ambuguity, because the previous sentence uses the same "Such a spell [...]" before it adds the "targets creatures [...] within". The echo of "such" in two sentences means that the "such" relatively unambiguously referrs to the first sentence.
So, given "Any spell of 5th level or lower" that is "cast from outside the barrier", then:
- It cannot affect creatures or objects within it.
- Creatures or objects can be targeted within it, but it has no effect on them.
- The area within the barrier is excluded from the areas affects by such spells.
And this holds even if cast using a higher level spell slot.
The next problem is Misty Step, and what "areas affected" means.
you teleport up to 30 feet to an unoccupied space that you can see.
Is the unoccupied space you can see an "area affected" by Misty Step? That could be interpreted either way. Either no (because it is not part of the "area of effect" of Misty Step), or yes (because it is an identified area -- an unoccupied space -- and having someone appear in an area sure seems to affects it).
If yes, then Misty Step does not work through the barrier. If no, then it works.
For Dimension Door:
You teleport yourself from your current location to any other spot within range. You arrive at exactly the spot desired.
There is less ambiguity here. The "spot" doesn't read as explicitly as an "area" as an "unoccupied space" does. You could stretch "area" to include the target location I suppose as well. But it is more questionable.
In the end, Misty Step working is questionable, but Dimension Door almost certainly works.
To address other arguments:
A Darkness spell cast from outside wouldn't darken anything inside, because "Such spells" is clearly not limited to spells that "target creatures or objects".
The rules for Forcecage have nothing to do with the rules for Globe of Invulnerability, and it having special rules about teleportation doesn't change how Globe works.
Dimension Door targets a spot, while Misty Step targets an unoccupied space. An unoccupied space is arguably an "area", but only arguably. Given that the two spells are basically doing the same thing, and that DD works, and that area is probably intended to refer to spells that impose effects on measured volumes (like 20' spheres or the like), I'd make MS work myself.