The ghost cannot enter the sphere from the ethereal plane.

Here is the full spell text for the 4th-level spell Otiluke's Resilient Sphere (emphasis mine):

A sphere of shimmering force encloses a creature or object of Large size or smaller within range. An unwilling creature must make a Dexterity saving throw. On a failed save, the creature is enclosed for the duration.

 Nothing—not physical objects, energy, or other spell effects—can pass through the barrier, in or out, though a creature in the sphere can breathe there. The sphere is immune to all damage, and a creature or object inside can’t be damaged by attacks or effects originating from outside, nor can a creature inside the sphere damage anything outside it.

The sphere is weightless and just large enough to contain the creature or object inside. An enclosed creature can use its action to push against the sphere’s walls and thus roll the sphere at up to half the creature’s speed. Similarly, the globe can be picked up and moved by other creatures.

A disintegrate spell targeting the globe destroys it without harming anything inside it.

- PHB 264

As noted, this spell lacks the distinction made in other spells such as the 5th-level Wall of Force and 7th-level Forcecage, in that it does not specify that it extends into the Ethereal Plane. However, the Dungeon Master's Guide states in its section on the Border Ethereal (emphasis mine):

A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don’t hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings.

- DMG 48

This would indicate that although not explicitly stated, as an effect made of magical force, the barrier does extend into the Border Ethereal. Because the barrier exists on the Ethereal Plane and does not allow anything to pass through, the ghost is not able to access the inside of the sphere through through the Ethereal Plane.

The ghost cannot enter the sphere from the ethereal plane.

Here is the full spell text for the 4th-level spell Otiluke's resilient sphere (emphasis mine):

A sphere of shimmering force encloses a creature or object of Large size or smaller within range. An unwilling creature must make a Dexterity saving throw. On a failed save, the creature is enclosed for the duration. 

Nothing—not physical objects, energy, or other spell effects—can pass through the barrier, in or out, though a creature in the sphere can breathe there. The sphere is immune to all damage, and a creature or object inside can’t be damaged by attacks or effects originating from outside, nor can a creature inside the sphere damage anything outside it.

The sphere is weightless and just large enough to contain the creature or object inside. An enclosed creature can use its action to push against the sphere’s walls and thus roll the sphere at up to half the creature’s speed. Similarly, the globe can be picked up and moved by other creatures.

A disintegrate spell targeting the globe destroys it without harming anything inside it.

As noted, this spell lacks the distinction made in other spells such as the 5th-level wall of force and 7th-level forcecage, in that it does not specify that it extends into the Ethereal Plane. However, the Dungeon Master's Guide states in its section on the Border Ethereal* (DMG page 48, emphasis mine):

A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don’t hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings.

This would indicate that although not explicitly stated, as an effect made of magical force, the barrier does extend into the Border Ethereal. Because the barrier exists on the Ethereal Plane and does not allow anything to pass through, the ghost is not able to access the inside of the sphere through the Ethereal Plane.

^{*It may be worth noting that this verbiage is only present in the DMG, and does not appear in the PHB/Basic Rules section on the Border Ethereal.}

The ghost can enter the sphere from the ethereal plane.

Here is the full spell text for the 4th-level spell Otiluke's Resilient Sphere (emphasis mine):

A sphere of shimmering force encloses a creature or object of Large size or smaller within range. An unwilling creature must make a Dexterity saving throw. On a failed save, the creature is enclosed for the duration.

Nothing—not physical objects, energy, or other spell effects—can pass through the barrier, in or out, though a creature in the sphere can breathe there. The sphere is immune to all damage, and a creature or object inside can’t be damaged by attacks or effects originating from outside, nor can a creature inside the sphere damage anything outside it.

The sphere is weightless and just large enough to contain the creature or object inside. An enclosed creature can use its action to push against the sphere’s walls and thus roll the sphere at up to half the creature’s speed. Similarly, the globe can be picked up and moved by other creatures.

A disintegrate spell targeting the globe destroys it without harming anything inside it.

As noted, this spell lacks the distinction made in other spells such as the 5th-level Wall of Force and 7th-level Forcecage, in that it does not specify that it extends into the ethereal plane. The walls of the Resilient Sphere exist only on the material plane.

The ghost's Etherealness ability reads (emphasis mine):

The ghost enters the Ethereal Plane from the Material Plane, or vice versa. It is visible on the Material Plane while it is in the Border Ethereal, and vice versa, yet it can't affect or be affected by anything on the other plane.

The barrier does not exist on the ethereal plane, and does not prevent the ghost's movement while there, and shifting back to the material plane within the border of the sphere does not pass through the barrier.

The ghost can damage the creature in the sphere

As noted above, the spell text reads:

...a creature or object inside can’t be damaged by attacks or effects originating from outside, nor can a creature inside the sphere damage anything outside it.

Once the ghost is inside the sphere this restriction no longer affects it and the ghost is able to attack and damage any other creature or object within the sphere, and vice-versa.

The ghost cannot enter the sphere from the ethereal plane.

Here is the full spell text for the 4th-level spell Otiluke's Resilient Sphere (emphasis mine):

A sphere of shimmering force encloses a creature or object of Large size or smaller within range. An unwilling creature must make a Dexterity saving throw. On a failed save, the creature is enclosed for the duration.

Nothing—not physical objects, energy, or other spell effects—can pass through the barrier, in or out, though a creature in the sphere can breathe there. The sphere is immune to all damage, and a creature or object inside can’t be damaged by attacks or effects originating from outside, nor can a creature inside the sphere damage anything outside it.

The sphere is weightless and just large enough to contain the creature or object inside. An enclosed creature can use its action to push against the sphere’s walls and thus roll the sphere at up to half the creature’s speed. Similarly, the globe can be picked up and moved by other creatures.

A disintegrate spell targeting the globe destroys it without harming anything inside it.

- PHB 264

As noted, this spell lacks the distinction made in other spells such as the 5th-level Wall of Force and 7th-level Forcecage, in that it does not specify that it extends into the Ethereal Plane. However, the Dungeon Master's Guide states in its section on the Border Ethereal (emphasis mine):

A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don’t hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings.

- DMG 48

This would indicate that although not explicitly stated, as an effect made of magical force, the barrier does extend into the Border Ethereal. Because the barrier exists on the Ethereal Plane and does not allow anything to pass through, the ghost is not able to access the inside of the sphere through through the Ethereal Plane.