Difference between 沒轍, 莫可奈何，沒辦法 Can anyone help me with any differences between those words? C-E dictionaries say "there's no way out" or "nothing can be done" for all of them, C-C dictionaries say about the same.

However, I was corrected using 莫可奈何 and 沒轍 wrong in these examples:

B: 還不就是我媽，三天兩頭就幫我安排相親，他明知道我最排斥相親這件事！唉！別人我還可以不理，偏偏他是我老媽，我也【莫可奈何】。

A: 都什麼時代了，你買還來相親這一套啊？！不過話是回來，天下父母心，做父母的總是為子女的終身大事，我也 【沒轍】，沒法幫你。真是難為你了。

I put 沒轍 for 莫可奈何 and vice versa. Can anyone explain the different notions of these two words? I added 沒辦法 as well, because maybe there are some similarities.

Thanks for all the help.
These three phrases differ in register, which affects how and when they will be used.

méi bànfǎ 沒辦法 is basic Mandarin and can be used in ordinary speech and writing without any issues arising.

mò kě nàihé 莫可奈何 is a highly learnèd idiom; a more common form is wú kě nàihé  無可奈何. As four-character Classical idioms, they have a certain formal "air" to them, even though 無可奈何 is pretty common. But it is a less basic expression than 沒辦法 — I would use 沒辦法 nine times out of ten, at least. I have never used 莫可奈何.

méizhé 沒轍 is highly colloquial and has a regional flavor. I wouldn't use it unless it's part of your normal regional accent.