These responses have provided some helpful examples for clarifying, so I’m glad the question was asked. Just here to ask:
You seem to swap which is the direct and indirect objects here–did you just mix it up, or am I missing something extremely subtle and critical? :')
The difference is that と implies a more reciprocal action.
友達に会った。 = I met my friend
友達と会った。 = My friend and I met each other
友達に話した。 = I spoke to my friend
友達と話した。 = My friend and I spoke with each other
I’m still not 100% clear, but this has actually helped a TON! Thank you so much!
I have basically narrowed it down to a verb with wo means the verb is “consuming” that object in which you are relating to it.
If I said “I read a book” the verb “to read” is consuming the object “book”.
And with ni, if I said “I spoke to my teacher” the verb “to speak” is something that isn’t consuming/using the teacher… It is something I am doing to ‘nothing’, but rather I am directing (could I even think of it as ‘performing on’?) the teacher.
Oh, and just wanted to mention, 話す is indeed transitive. It’s just that the sentence in question had an indirect object, and not a reference to the content of what was being spoken.
日本語を話す to speak Japanese
日本語で前の事を話す to speak about the thing from before in Japanese
事実を話す to speak the truth
Oh yeah, true!
Huh–does that relate toと’s role as ‘and’, with the other person inferred from context? Something like “My friend and (I, implied) spoke”? …Probably that’s just oversimplifying it a bit, and either way I guess it’s kind of a pointless question, though, since functionally that’d equal out to ‘with’.
Other thought: Would saying something like 友達を会った come off as slightly rude, like you’re reducing your friend to an object or something that had no choice in the matter? I’m guessing it’d probably just sound kind of off and jarring, the same way saying something like “I met at my friend” might sound in English.
It’s just not grammatical. It would be interpreted as a (common) mistake and nothing more.
I was just trying to explain it in English; once you understand it, I think you can apply it to Japanese just as easily.
Also, to be clear, “object” in the grammatical sense doesn’t mean “inanimate thing” but simply “the party that has the verb done to it”.
I wouldn’t say it’s a pointless question. It’s completely valid 
. Below example from @Saida illustrates it super well:
In this case と would indeed mean “and” the way you think about it. But otherwise I wouldn’t mix them I guess (the と with verbs and と to join nouns).
A direct object is the thing receiving the action in a very direct sense.
Because both parts of speech are objects of a verb, it is true that both objects are receiving the action of the verb in a sense, but the way they are receiving it is different.
In the sentence “I spoke to my teacher”, the teacher is being spoken to, but the teacher is not being spoken because that doesn’t make any sense. Presumably, words are being spoken, but it was left unsaid.
Another example is “I spoke English with my teacher”. The teacher is still the indirect object because they are being spoken to, but now ‘English’ is the direct object because it is what is being spoken.
Similarly, ‘I give a dog a bone’. The bone is being given while the dog is being given to, so the bone is the direct object, and the dog is the indirect object.
I figure out direct objects (in English) by asking the question “What is [verb]ed?” eg. “What is spoken?” “What is given?”
I hope that helps, at least for the English version of direct/indirect objects! Japanese works very similarly.
In practice I still think you’re better off either learning your transitives and intransitives and then just using the matching particle, or just learning through immersion, but…
Another example might be “I kicked a ball” vs “I kicked a ball at the wall”.
“I kicked” acts on the ball, the wall is pretty much unrelated to that, except that it happens to be in the direction I kicked. If you wanted to make the sentence act on the wall, you’d have to change it to something like “I hit the wall with the ball”.
To demonstrate how the indirect object is optional, but the direct one isn’t, see what happens when you delete each one:
And finally, an intransitive example might be “I rise toward the sky”. In this case the direct object is the same as the subject (me). I’m quite clearly not doing anything to the sky, it’s just in the direction I’m moving. “I rise” doesn’t change the meaning, just loses some information.
It’s basically the same concept in Japanese, but a bit harder to demonstrate because they liberally omit bits of the sentence…also I need to go to bed now…
- If a verb is transitive, it needs a direct object, and the only possible way of marking that is with を.
- Intransitive and transitive verbs can both optionally take an indirect object. That indirect object in some sense recieves something as a result of the action of the verb, but the verb does not act on it . I think @chemifox did a good job of giving examples of this.
So… intransitive and transitive verbs both requires a direct object, but tacking on an indirect object is optional?
To be clear, the direct object can also simply be implied. Using a transitive verb means there’s a direct object, whether it’s marked explicitly by を, implied from context, or completely unknown.
Intransitive verbs cannot take a direct object, period.
In Japanese, not in general (you can’t do it in English, for instance).
This is why I gave me examples only in English. the topic is confusing enough without that “minor” detail 
Ayeaye–I originally left out the ‘object’ part but wound up pushing a bit too hard to get what I was thinking across. Thanks for making sure to clarify!
Ah yeah, true! In the end I guess it’s just something to keep in mind–I tend to overfocus on particles a bit, so this might help with not tripping up on “wait a minute, is this ‘and’ or ‘with’ here” if the rest of the context means that either possibility would fit in alright.
actually yet another way to think about it: に is a preposition, same as “to” or “at” or “with” or whatever. を is just the accusative case marker*
*usually…there’s just too many caveats when it comes to Japanese
Well, strictly speaking, に is a postposition.
As with all particles, for that matter.
The OP is trying to understand Japanese. So “in Japanese” is what matters most… Besides, omitting particles in Japanese is not remotely a minor detail. I’d hate for the OP to mistakenly think you must include the direct object in all cases.