These three words can be synonyms, but have slightly different connotations.
First, travel is usually a verb...
I will travel to Washington DC.
...but not always. In common speech (at least as far as I am familiar), when used as a noun, it is used in its plural form:
How were your travels?
Compared to the substantially equivalent sentences:
How was your trip?
How was your journey?
One could also ask How was your travel?, but it this would have a more specific meaning, for instance, "How was your flight from New York to L.A.?" as opposed to "How was your entire journey, and the time you spent in L.A.?"
Trip and journey are more closely interchangeable, and vary mostly in duration, distance, and formality.
A trip can be a short journey. One can take a trip to the store, but it would be unusual (except in poetic exaggeration) to take a journey to the store
A journey would often imply a longer (in terms of time and/or distance) trip, perhaps to multiple destinations, or with a greater sense of unknown. A journey may not be fully planned out ahead of time.
A business conference to Seattle would probably be described as a trip, whereas a family vacation road-trip from Nebraska, through the Colorado Rockies, camping in Nevada, then stopping in Las Vegas and returning through Oklahoma and Kansas, might be described as a journey.
Often, in colloquial English (at least in the U.S.), trip is far more commonly used than journey, even when describing long/epic travels.
Both trip and journey can also be verbs, but when used as verbs they are not interchangeable. To journey is to engage in the act of journeying:
We journeyed to the Grand Canyon.
However to trip is to cause someone to stumble or lose their balance.
She tripped the thief with her cane.
I tripped over the dog.
To trip up has the additional connotation of causing someone to blunder:
The reporter tripped up the senator.
There are also some additional cases where trip and journey cannot be interchanged in some common expressions:
- A guilt trip
- A high brought on by recreational drugs can be called a "trip."
- Trippy -- slang; reminiscent of the "trip" (high) brought on by recreational drugs; especially LSD
First, that description of "been to" and "gone to" is mostly accurate. However, to "have gone to" a place can mean that you're no longer there, the same as if you "have been to" a place. (There are other subtle differences between these two expressions; see the previous edit to see them.)
It seems to me that the same logic doesn't quite apply for "have been on a trip"/"have gone on a trip". The latter two are mostly interchangeable, although there might be slightly different nuances about the "default" interpretation. I'll quickly go through some examples.
Both of the "on a trip" expressions can be used to mean you're still on that trip:
(1) I've been on a trip to Europe these past six months.
The speaker is still in Europe.
(2) I've gone on a trip to Europe and I won't be back till August.
The speaker is still in Europe.
And both of them can mean that you are not still on that trip (helped by including the word "ever"):
(3) Have you ever been on a trip to Europe?
The speaker is no longer in Europe.
(4) Have you ever gone on a trip to Europe?
The speaker is no longer in Europe.
So the two expressions pattern like "been to" and "gone to" except that "been to" would not work where "been on a trip to" works in sentence (1):
(1b) ✗? I've been to Europe these past six months.
If this works at all, it means the speaker went in the past six months and is no longer in Europe.
Since both meanings are possible, what's the default interpretation without context?
In British English, I'd say it's the same as "been to" and "gone to". In North American English, I would say it's the reverse. (This is based on my and my relatives' usage. I am AmE and my relatives BrE.)
(5) I've been on a trip to Europe.
BrE: The speaker is probably back. AmE: The speaker is probably still there.
(6) I've gone on a trip to Europe.
BrE: The speaker is probably still there. AmE: The speaker is probably back.
To generalize a bit, I imagine that both the above pattern and the account you cited in your question owe a lot to the fact that in British English, "to have been" is often used in the sense that NA English uses the simple past.
— "Was there anything in the mailbox?"
— "I've just been. There wasn't anything." (BrE)
— "I just went. There wasn't anything." (AmE)
Even two phrases that appear identical can mean two different things depending on the region.
"I've been swimming today."
usually means "I went swimming earlier today." (BrE)
usually means "I was swimming earlier today." (AmE)
P.S. Another minor difference between "been to"/"gone to" and "been on a trip"/"gone on a trip" is that the "been" in "been on a trip" can be conjugated in any tense:
✓ Next week I'll be on a trip to Europe.
✗ Next week I'll be to Europe.
✓ Right now I am on a trip to Europe.
✗ Right now I am to Europe.
Best Answer
"I have a trip", in that form, is unusual. If you look at the actual texts that your Ngram results are taken from, most of them use "have a trip" as part of longer expessions, like
"have a trip coming up"
"have a trip planned"
"had a trip cooked up"
"had a trip scheduled."
"had a trip to take"
There are some examples of "I had a trip" with the meaning of
"I went on a trip". or "I took a trip.", but they are so rare that I would call it unidiomatic.