Coordinating conjunction for connecting list items

In compliance with the Oxford comma when listing three or more items a comma is used between the items and before and.

What if in a list of three items two of them have a word in common (edge computing and cloud computing = edge and cloud computing), how should the commas be used?

We discussed task offloading, edge, and fog computing.

Edge doesn't really make sense, so if I delete the comma after it, do I get a list of two items instead (view bellow)?

We discussed task offloading and edge and fog computing.

Furthermore, what if a fourth item is added:

We discussed network latency, task offloading, and edge and fog computing.

or does the other way round make more sense (both in terms of general clarity and in terms of grammatical correctness):

We discussed edge and fog computing, task offloading, and network latency.

Short Answer

You are getting into trouble with comprehension because you are combining two of the nouns.

Without taking any shortcuts that could lead to confusion, the following will always be correct and understandable:

• ✔ We discussed task offloading, edge computing, and fog computing.
• ✔ We discussed network latency, task offloading, edge computing, and fog computing.

It's better to be understood than to make something succinct at the cost of comprehension.

Taking any kind of shortcut might cause confusion. Any discussion of what shortcut should be used is often a matter of style. While some styles are common, not everybody necessarily uses the same one. So, there is no single answer that is always objectively correct.

However, skip to the third section of this answer if you want a stylistic answer.

Intermediate Discussion

There is a possible problem with the assumption that even the simple edge computing and fog computing can be turned into edge and fog computing without confusion.

Determine the number of types of items being discussed in the following two sentences:

1. We discussed edge and fog computing.
2. We discussed peanut butter and jelly sandwiches.

We can assume something, but only because of context and experience:

1. We discussed (1) edge ^computing and (2) fog computing.
2. We discussed (1) peanut butter and jelly sandwiches.

However, it's not beyond the realm of possibility that somebody could actually mean something different:

1. We discussed (1) edge and fog computing.
   
   We discussed a single area of computing that involved the combination of edge technology and fog technology.
   
   
2. We discussed (1) peanut butter sandwiches and (2) jelly sandwiches.
   
   We discussed two types of sandwiches, one made with just peanut butter, and the other made with just jelly.

So, even the assumption that edge and fog computing is taken to mean two different types of computing could be faulty. In which case, refer back to the start of this answer, and don't combine them.

But let's assume there is no misunderstanding, and that everybody understands the meaning of edge and fog computing, and that it describes two different things. Commonly, such combinations are made all the time.

Unless somebody is talking about peanut butter and jelly sandwiches, it's understood that the conjunction is just a shortcut to combine the description of two different things.

Possible Styles to Avoid Confusion

If you are to combine two items with a conjunction and then add more items, there are a couple of ways that are commonly accepted.

✘ We discussed task offloading, edge, and fog computing.

As mentioned in the question, you cannot do it this way because it leads to too much confusion over the use of edge between commas.

Funnily enough, the commonly accepted way of doing this is already provided in the question with its example sentences of four items. Applying that to just three items, this is what we would normally see:

• ✔ We discussed task offloading, and edge and fog computing.
• ✔ We discussed edge and fog computing, and task offloading.

Despite the normal conventions of conjunctions and serial commas, either of the above styles are often accepted.

But there is an alternative:

• ✔ We discussed task offloading, as well as edge and fog computing.
• ✔ We discussed edge and fog computing, as well as task offloading.

The use of as well as breaks the flow that the series of conjunctions and serial comma previously struggled with. Other phrases such as in addition to could also be employed.

Note that, depending on style, the comma used in the above two sentences could be omitted.

This works when there are three items.

When it comes to four or more items, at least two of which are paired together with a shortening conjunction, you can also make use of semicolons—something that every major style guide recommends when there are multiple such items.

The use of semicolons is even more necessary when there are two or more pairs of such items:

• ✔ We discussed network and local latency; task offloading; edge and fog computing; cats; and peanut butter and jelly sandwiches.

Because of the number of items, semicolons are easily employed. Further, it's commonly understood that peanut butter and jelly sandwiches is being used in a way that's different from the other combined list items.