I would allow players to make the spell cover any shape they wanted, provided that shape is simply defined, contiguous, has no "islands" or "doughnut holes", and no part of it is further than 60ft from the point they touch while casting the spell. By "simply defined", I mean simple shapes (cube, sphere, etc), or anything that can be expressed simply and obviously, like "inside the house" or "the area under the bridge".

I came to this ruling because it leaves maximum scope for the players to do what they want, while minimising the number of ways that it can become complicated, boring or overpowered.

Analysing the rules

Generally, where things are vague in 5e, the best way to approach it is thus:

• Do other rules have anything related to say?
• How would players generally be expected to use it?
• Which interpretation causes fewer complications?
• Which interpretation protects against abuses or ways to bypass balancing mechanisms (action economy, spell slots, etc)?

Related rules

The section on spellcasting doesn't mention how to handle spells that don't use one of the listed shapes. However, the alarm spell can be cast to cover "an area within range that is no larger than a 20-foot cube", which means there is precedent for choosing your own shape of area, within certain size constraints.

Expected use

I'd expect players to use hallow to protect areas like the inside of a place they're staying in - a house, a castle, a cave, whatever. This could be any shape, really, and as a DM there's no reason to want to spoil that for them.

Complications

Circles don't tessellate, and the players may wish to cover larger areas. Handling the bits of a circle that protrude out through the walls of a square house may be tricky (if you rule that this happens).

Balancing

The 24-hour casting time and 1000GP cost protect against serious abuses, and with those in place, I can't see a particular way that one shape is "overpowered" compared to another.

Ruling

Given these observations, I see no problem in letting players choose any shape they like. Of course, the spell says "you touch a point, and infuse an area around it", so no part of that shape can be more than 60ft from the point they're touching. This means that to cover a corridor that's 120ft long, you'd have to cast the spell from the middle. For the sake of keeping things simple, I'd probably also say that the area can't have "islands" in it - for example, you couldn't hallow a doughnut shape; you'd have to cover the bit in the middle. (This also prevents you from using hallow to trap things in the middle, which is the only thing I can see that might be open to abuse.) Likewise, you can't use one casting of hallow to cover two separate but unconnected areas, even if both of them fall within the spell's range. The hallowed area must be contiguous.

Reasoning

Letting the player pick the shape covers their intended uses, while also preventing situations that are either fiddly to manage or detrimental to the game's balance. In other words, it streamlines the playing of the game without blocking anything that's fun or adding anything that makes it less fun - which is the mark of a good rule.

For some examples, consider the following scenarios:

• The players want to hallow the inside of a small house, without having gaps at the corners or weird curved segments of hallowed ground outside it. Letting them choose the shape lets you divide it simply into "inside = hallowed" and "outside = not hallowed".
• The players want to hallow a larger area. Letting them pick the shape lets them choose a shape that tessellates. If you're playing on a square grid, they can hallow cubes; if you play on a hexagonal grid, they can hallow hexes. If they want, they can pick other shapes that fit the terrain, like "up to the edge of the cliff" or "120ft of road".
• The players want to hallow a small building, but the building is shaped such that they can't see all of it at once (perhaps three sides of a square). Letting them pick the shape lets them hallow it all in one casting provided that it's small enough. Given two buildings of equal floor area where one can be hallowed in one casting but the other takes several because of its shape is needlessly complicated for little gain in entertainment value.

The Wizard may Ready an action to cast a spell setting the trigger to be when the orcs have finished moving.

What will occur on the Orcs' turn is they will move (potentially in a cluster), the Wizard will cast the spell, and the Orcs will do something with their Action. It should be noted, they might respond to the spell by using their Action to dash, which would let them run away; they could choose to just attack the Wizard and attempt to break his concentration, or something else.

In addition, your question suggests that you might be confusing a Round and a Turn, which are separate and distinct things from a timekeeping perspective. A Turn is an individual's activities that occur during a Round. A Round is the sum of all the creatures' activities and always equals 6 seconds. Some effects will say that they occur at the beginning or end of a Turn, which refers to the individual creature; other effects will indicate they occur over some number of rounds (most often represented with time increments like 1 minute).

So for your specific issue, the damage is dealt at the end of a creature's turn. This is an individual determination. For example, were there Orcs and Wizards in this fight, the sphere deals damage to the Orcs only if they qualify (are within 5' of the sphere) at the end of the Orcs' turn. At the end of the Wizards' turn, the same assessment is made to determine if the Wizards take damage. The spell also permits an additional effect that allows the Wizards to attack with the sphere more directly during their turn.

In tight spaces, it's possible to deal a lot of damage with this spell passively by virtue of its presence, but in most fights it's probably only dealing damage on the Wizard's turn. Otherwise, it's serving to deny access to an area because most folks don't want to end their turn taking 2d6 fire.

Regardless, if the sphere is still adjacent to any Orcs at the end of their turn, they will suffer the effects as described in the spell.