To a linguist, there is an obvious difference between verbal and oral: only the first word can be used to mean “pertaining to a verb”. But for people who don’t talk about parts of speech so often, the more relevant question is whether verbal can refer to spoken language (as opposed to written language), or if it can only refer to the more general sense of all language:
(1a) The written warning is primarily the verbal warning put in writing […]
(1b) […] general verbal skills, such as verbal fluency, ability to understand and use verbal reasoning, and verbal knowledge.
Some people insist that verbal can’t be used as in (1a). Verbal is derived from the Latin verbum, meaning “word”, and that means that it only distinguishes things involving words from things not involving words. This is the usage in (1b), where verbal reasoning is implicitly differentiated from mathematical reasoning, or spatial reasoning, or any other form of reasoning that is not based in words. Clearly this is a valid usage of verbal.
And, while we’re at it, we can quickly agree that oral would be inappropriate for the usage in (1b). “Oral knowledge”, for instance, is specifically knowledge that is spoken aloud, and I really can’t see that being the intended meaning. I think we can also all agree that oral is definitely appropriate for the usage in (1a). So what we have a is 2×2 chart, with three of the values filled in:
|verbal||YES (1b)||? (1a)|
|oral||NO (1b)||YES (1a)|
The only remaining question is whether verbal is allowable in that last cell, with the meaning “spoken”. And the answer is yes, and it has been almost since verbal‘s first appearance in English. The Oxford English Dictionary first attests verbal in 1483, but at that point it modifies people. William Caxton writes:
“We be verbal, or ful of wordes, and desyre more the wordes than the thynges.”
The first attestation of verbal meaning “composed of words” comes between 50 and 100 years later, in either 1530 or 1589.* And the first attestation of verbal meaning “conveyed by speech” comes in 1617:
“The Chamber of the Pallace where verball appeales are decided […]”
This meaning has persisted. I looked at the Corpus of Historical American English (COHA) for the most common nouns to follow verbal over the past 200 years. The two most common collocates were communication and expression, each with 43 hits. Unfortunately, looking at the contexts in which these were used, it’s hard for me to tell which meaning was intended. But the third most common collocate, message, appears 40 times, spread out over the past two centuries. And these are pretty unambiguously examples of the “spoken” meaning, because it’s rare that you’d need to distinguish message delivered in words from those that aren’t. For instance:
“His reply was this verbal message: ‘Wait — and trust in God!'” 
“The verbal message is the key to the written one.” 
I don’t have numbers on the relative usage of the two meanings of verbal, so I’m not going to try to say that one is more common than the other. But it is pretty clear that the “conveyed by speech” meaning is valid.
Does this acceptability mean that you should unquestioningly use it in this way? Not necessarily; there is a potentially significant ambiguity here, so it’s not the best choice in all situations. On occasion, it will matter whether verbal means “conveyed by speech” or “involving words”. If I write to a tutor and ask them to improve my verbal skills, it may be ambiguous as to whether I’m looking for instruction in public speaking or vocabulary building. That’s a trivial example, but in legal contexts, it’s probably better to refer to oral contracts, warnings, etc. than verbal ones, just to avoid the ambiguity.
In most cases, where this ambiguity is small or unimportant, you can and should use whichever feels better to you. You can freely swap between the two meanings in different contexts, as I do. A lot of the time, the context (especially what noun verbal is modifying) will clarify things. So in the end, our chart becomes:
Summary: Verbal can refer either to anything delivered in words or something that is specifically spoken. This latter usage is sometimes condemned as modern sloppiness, but it’s been persistently attested for 400 years. The ambiguity is generally not sufficient to be problematic, so it’s only in cases where precision is paramount that the latter usage should be avoided.
*: The 1530 attestation is listed under this definition, but its usage seems to me identical to Caxton’s usage, modifying people. The 1589 attestation is unambiguously referring to language, referring to “verbale sermons”.