A tricky question

This question concerns the verbs 行く、来る、and 帰る (and possiblly others).
The main thing I am trying to figure out is whether these verbs include an intrinsic sense of being completed. When I say ロンドンに行く, does it take me all the way to London? It is difficult to express this without using the ～ている form. For example, the following sentence:
彼は教室に行っている。
Which of the following does the above sentence mean？:
He is on the way to the classroom. 彼は教室に行く途中だ。
OR
He is in the classroom. 彼は教室に行って（その動作を終えて）、教室にいる。

And how about this example?:
彼女は家に帰っている。
Which of the following does the above mean?:
She is on the way home. 彼女は家に帰る途中だ。
OR
She is home. 彼女は家に帰って（その動作を終えて）、家にいる。

I won't bother doing one for 来る because I believe it would be redundant. If it's not, please let me know, though.
I would appreciate any help or advice from anyone on the topic. It's gonna keep me up tonight.

Usually, to indicate that the going is not complete, one uses 向かっている instead of 行っている. Sort of like saying "He is headed to the classroom" instead of "He is going to the classroom".

In most cases, situational of course, but I think Mike's suggestion stands when you want to emphasize going, but not yet there. Otherwise, would mean in the act of doing (as the verb tense states).

I suppose it can be either as well. To get across the idea of a future plan, such as being in Tokyo a week I'd probably put it something like this 「一週間東京に行っている」「一週間東京に行って来る」など. On the other hand "(have/has) come" is often seen as "来ている" (コンビニエントストアに買い物に来ている人も客です)
(今年は日本に来ている人が多いです), clearly implying having arrived or already staying.

Although please anyone correct either of these examples that are unnatural.

Thanks for the responses so far. I've studied Japanese for a long time and for some reason, this "double" meaning never really clicked in my head before last night, when another long-time Japanese learner friend of mine and I were having a heavy debate on some other grammar points.

Looking at the 広辞苑 provides these two definitions (amongst others) for 行く：
1 目的地に向かい進む。
2 目的の所に到達する。

As you can see, the definitions are very different. I think I've underestimated this verb for a long time.

Any native speakers able to shed some more light on the subject?

彼は教室に行っている。
Which of the following does the above sentence mean？:
He is on the way to the classroom. 彼は教室に行く途中だ。
OR
He is in the classroom. 彼は教室に行って（その動作を終えて）、教室にいる。

And how about this example?:
彼女は家に帰っている。
Which of the following does the above mean?:
She is on the way home. 彼女は家に帰る途中だ。
OR
She is home. 彼女は家に帰って（その動作を終えて）、家にいる。

Click to expand...

I would say in these cases in particular the best English translation is "has gone to class" or "has gone (returned?) home," of course equally ambiguous on a precise location unless that becomes important for some reason (the person is being sought) or is something the context will help clarify.

こんにちは、オロチさん！

I would like to just add my two cents' worth.

The word 行く does have two meanings, as you found in Kojien. This is because many words in Japanese are defined by context, probably many more than in English. In trying to explain words and usage in Japanese, I have recently realized how heavily context-dependent Japanese is! I think this is especially true for common words like 行く and 帰る. For more detailed description, you use words such as 向かう, as Mike suggested. If you want to say that a person has definitely arrived at a location, you use the verb 着く（つく）. 出る is used to describe a person has left (and is heading for some specified or unspecified location).

In using 行く or 来る, you have to determine the meaning from context. Please note also that there are instances in which the speaker or writer use such words to be vague deliberately.