Per the description of the spell (emphasis mine):

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.

Can a creature within the barrier cast spells out from it, or does the barrier block ALL spells of the appropriate levels from going either way? A strict reading of the description seems to lend itself to the interpretation that the globe is a one-way barrier; i.e., spells can be cast out, but not in. Have there been any rulings from Mearls, Crawford, etc.? I've done some searching online and there doesn't seem to be a clear consensus.

The part you put in bold makes me think that they wanted it to be understood that the barrier would also block "a point which you can see" spells. For instance, someone saying that they will cast Darkness inside the barrier expecting it to still affect something due to it being cast in front of an enemy and not "on" them. I would say an unintentional side effect would by the inability to cast 5th or lower spells that must take effect/originate within the barrier but, casting a spell that can manifest outside the caster's location is fair game imho.

You can cast out of it. The part that you bolded means that AoE spells don't affect the inside of the globe. So dropping a 3rd level fireball just outside the globe doesn't do anything to the interior.

Quote from Wtfdndad >>

The part you put in bold makes me think that they wanted it to be understood that the barrier would also block "a point which you can see" spells. For instance, someone saying that they will cast Darkness inside the barrier expecting it to still affect something due to it being cast in front of an enemy and not "on" them. I would say an unintentional side effect would by the inability to cast 5th or lower spells that must take effect/originate within the barrier but, casting a spell that can manifest outside the caster's location is fair game imho.

 
Right, this brings up an interesting question: what if a caster WITHIN the barrier casts an AoE spell with a radius greater than the globe, but centers it on themselves? 

What if the caster has resistance or immunity to, say, fire damage, and there are enemies all around the globe - and the caster drops a fireball, cast a 3rd level spell, centered on themselves or very near to themselves? Does it go off and affect everyone? Or just those outside the barrier? Or those just inside the barrier?

Notice the second and third sentences use "such a spell" and "such spells." All of these lines are referring to spells cast from outside the barrier. Thus spells cast from within the barrier would still behave as normal, including a fireball cast by you targeting any point inside or outside the barrier.

Compare the wording with Otiluke’s Resilient Sphere, which very specifically notes that the barrier works both ways.

"Any spell of 5th level or lower cast from outside the barrier can't affect creatures or objects within it,"

That's the main rule here. So casting Fireball on yourself would still damage you, as it wasn't cast outside the barrier. However, it would also hit everyone around you as well. If you have immunity you should probably be doing this without bothering with the globe tbh!

Quote from scatterbraind >>

Notice the second and third sentences use "such a spell" and "such spells." All of these lines are referring to spells cast from outside the barrier. Thus spells cast from within the barrier would still behave as normal, including a fireball cast by you targeting any point inside or outside the barrier.

Compare the wording with Otiluke’s Resilient Sphere, which very specifically notes that the barrier works both ways.

 This.  any casting from inside the globe works normally, no matter where it is targeted or where its AoE goes.  the globe only impacts 5th and lower level spells originating from outside of itself.  It's basically a one-way antimagic field for lower level spells.  

Yeah, everything the globe blocks is from outside going in. It makes no reference (subtle or overt) to spells cast from inside, thus has no effect on them one way or the other.

Of course it also only blocks spells and not weapons or creatures, so it is far from overpowered. Good in mage duels, that's about it.

Quote from DxJxC >>

Of course it also only blocks spells and not weapons or creatures, so it is far from overpowered. Good in mage duels, that's about it.

 
Yes, and it doesn't suppress magic (a magic sword is still a magic sword inside the barrier).

Quote from Xukuri >>

Quote from Wtfdndad >>

The part you put in bold makes me think that they wanted it to be understood that the barrier would also block "a point which you can see" spells. For instance, someone saying that they will cast Darkness inside the barrier expecting it to still affect something due to it being cast in front of an enemy and not "on" them. I would say an unintentional side effect would by the inability to cast 5th or lower spells that must take effect/originate within the barrier but, casting a spell that can manifest outside the caster's location is fair game imho.

 
Right, this brings up an interesting question: what if a caster WITHIN the barrier casts an AoE spell with a radius greater than the globe, but centers it on themselves? 

What if the caster has resistance or immunity to, say, fire damage, and there are enemies all around the globe - and the caster drops a fireball, cast a 3rd level spell, centered on themselves or very near to themselves? Does it go off and affect everyone? Or just those outside the barrier? Or those just inside the barrier?

Globe of Invulnerability is fairly explicit, so I'll cover this and your OP:

1. "Can a creature within the barrier cast spells out from it or does the barrier block ALL spells of the appropriate levels from going either way?"
   
   • A creature within the barrier can cast spells, regardless of whether the spell is being cast "out" or staying within the globe.  The text simply doesn't stop them.
     • Any spell cast within the barrier acts completely normally in every way, as if the globe did not exist.
   • No, the barrier does not block all spells going in both directions - in fact, it doesn't block spells going in either direction.  It excludes its own area from other areas of effect and renders creatures and objects immune to the effects of "incoming" spells.  If someone outside the globe casts sickening radiance on a point inside the globe, the radiance field comes into being around the globe - the spell isn't blocked, the area inside the globe is simply excluded.
2. "What if a caster WITHIN the barrier casts an AoE spell with a radius greater than the globe, but centers it on themselves?"
   • Nothing special - as explicitly spelled out in the spell's text, Globe only interacts with spells cast from outside the Globe.  Any spell not cast outside the Globe is not interacted with by the Globe.
3. "What if the caster has resistance or immunity to, say, fire damage, and there are enemies all around the globe - and the caster drops a fireball, cast a 3rd level spell, centered on themselves or very near to themselves? Does it go off and affect everyone? Or just those outside the barrier? Or those just inside the barrier?"
   • See 2.  The fireball goes off normally, because it was cast inside the globe, and hence the globe has no interaction with the fireball at all.
   • If you have a second caster in the party, you can have them fireball the globed caster from outside the globe, and the globe will outperform sculpt spells or careful spell - the globe will keep the globed caster safe as the fireball goes off around them.