So, let's see the following examples,
教 + (英)语 => teach the language which is used among English(American) people.
教 + (法)语 => teach the language which is used among French people.
教 + (英语是第二)语 => Mandarine speakers may wonder what "英语是第二" is.
Here, you may have two options to make the sentence more clear.
1. I teach the "English Is The Second Language" program online.
2. I am the teacher of the "English Is The Second Language" online program. (Imply that you can teach the program)
Otherwise, you need to keep the "ESL" as it is. I mean, the abbreviation form.
In addition, Mandarin speakers are used to naming something/somebody with nouns or the composition of determiner and noun(s).
As a result, “英语是第二”语 doesn't conform to the rules of naming shown above.
ESL is not a well-known thing among common people in China, and using the translation of its full name sounds very awkward. You'll probably have to refer to it by "ESL" and then explain what it is, unless you are sure the person you're talking to is familiar with it.
I think simply saying 我在線上教英文。 would suffice. Hearing this, people(at least here, and I guess even across the world?) would presume that you teach ESL online. I am not sure if it's common for native English speakers to learn English online. Of course, it's nothing wrong with a longer version like what Simon (#2) suggests.
Yes, if someone is teaching English online, it is normally ESL (but teaching ELA (English language arts--for native speakers) is also possible... especially during COVID where a lot of courses are taught online!).
I know that some technological terms are different between Mainland China, Taiwan (and Hong Kong?).
Is 在网上 more common in 大陆 and 在线上 (Is "上" optional here?) in 台湾? or are both terms used in both places?