I have informed the referees about the letters.

is proper diction and sounds natural.

I have informed the referees regarding the letters.

is also correct, but perhaps a little less natural. So I would choose the first. (If you "wrote" or "spoke with" instead of "informed", it would sound completely natural with "regarding" - these are just more common.)

I have informed the referees in respect of the letters.
I have informed the referees with reference to the letters.
I have informed the referees respecting the letters.
I have informed the referees on the subject of the letters.

All of these are incorrect use and either sound wrong or awkward or do not convey the same meaning! Here's how to use these properly:

I have talked to the referees with respect to the letters.

The propositions are incorrect above - the phrase is "with respect to, not "in respect of". People would understand you, but it will sound wrong.

I have informed the referees, with reference to the letters.

This is correct usage, but different meaning. The speaker has informed the referees about /something else being discussed/, which is contextual, and additionally made reference do the letters while doing so. You would not say "with reference to" if there was not something that the "reference" came along "with".

I have informed the referees of the subject of the letters.

You can also "inform about" the letters, but "inform on the subject of" sounds awkward, the proposition "on" clashes. You could "speak on the subject of", however, if addressing an audience.

Perhaps try to avoid "apropos" and "vis-a-vis". Both examples in the comments are correct use, but they are both somewhat archaic or extra-formal, and "vis-a-vis" might be confused to imply that you talked to someone in-person or face-to-face if not used correctly.

I have informed the referees about the letters.

is proper diction and sounds natural.

I have informed the referees regarding the letters.

is also correct, but perhaps a little less natural. So I would choose the first. (If you "wrote" or "spoke with" instead of "informed", it would sound completely natural with "regarding" - these are just more common.)

I have informed the referees in respect of the letters.
I have informed the referees with reference to the letters.
I have informed the referees respecting the letters.
I have informed the referees on the subject of the letters.

All of these are incorrect use and either sound wrong or awkward or do not convey the same meaning! Here's how to use some of these properly:

I have talked to the referees with respect to the letters.

The propositions are incorrect above - the phrase is "with respect to, not "in respect of". People would understand you, but it will sound wrong.

I have informed the referees, with reference to the letters.

This is correct usage, but different meaning. The speaker has informed the referees about /something else being discussed/, which is contextual, and additionally made reference do the letters while doing so. You would not say "with reference to" if there was not something that the "reference" came along "with".

I have informed the referees of the subject of the letters.

You can also "inform about" the letters, but "inform on the subject of" sounds awkward, the proposition "on" clashes. You could "speak on the subject of", however, if addressing an audience.

Perhaps try to avoid "apropos" and "vis-a-vis". Both examples in the comments are correct use, but they are both somewhat archaic or extra-formal, and "vis-a-vis" might be confused to imply that you talked to someone in-person or face-to-face if not used correctly.

I have informed the referees about the letters.

is proper diction and sounds natural.

I have informed the referees regarding the letters.

is also correct, but perhaps a little less natural. So I would choose the first. (If you "wrote" or "spoke with" instead of "informed", it would sound completely natural with "regarding" - these are just more common.)

I have informed the referees in respect of the letters.
I have informed the referees with reference to the letters.
I have informed the referees respecting the letters.
I have informed the referees on the subject of the letters.

All of these are incorrect use and either sound wrong or awkward or do not convey the same meaning! Here's how to use these properly:

I have talked to the referees with respect to the letters.

The propositions are incorrect above - the phrase is "with respect to, not "in respect of". People would understand you, but it will sound wrong.

I have informed the referees, with reference to the letters.

This is correct usage, but different meaning. The speaker has informed the referees about /something else being discussed/, which is contextual, and additionally made reference do the letters while doing so. You would not say "with reference to" if there was not something that the "reference" came along "with".

I have informed the referees of the subject of the letters.

You can also "inform about" the letters, but "inform on the subject of" sounds awkward, the proposition "on" clashes.

Perhaps try to avoid "apropos" and "vis-a-vis". Both examples in the comments are correct use, but they are both somewhat archaic or extra-formal, and "vis-a-vis" might be confused to imply that you talked to someone in-person or face-to-face if not used correctly.

I have informed the referees about the letters.

is proper diction and sounds natural.

I have informed the referees regarding the letters.

is also correct, but perhaps a little less natural. So I would choose the first. (If you "wrote" or "spoke with" instead of "informed", it would sound completely natural with "regarding" - these are just more common.)

I have informed the referees in respect of the letters.
I have informed the referees with reference to the letters.
I have informed the referees respecting the letters.
I have informed the referees on the subject of the letters.

All of these are incorrect use and either sound wrong or awkward or do not convey the same meaning! Here's how to use these properly:

I have talked to the referees with respect to the letters.

The propositions are incorrect above - the phrase is "with respect to, not "in respect of". People would understand you, but it will sound wrong.

I have informed the referees, with reference to the letters.

This is correct usage, but different meaning. The speaker has informed the referees about /something else being discussed/, which is contextual, and additionally made reference do the letters while doing so. You would not say "with reference to" if there was not something that the "reference" came along "with".

I have informed the referees of the subject of the letters.

You can also "inform about" the letters, but "inform on the subject of" sounds awkward, the proposition "on" clashes. You could "speak on the subject of", however, if addressing an audience.

Perhaps try to avoid "apropos" and "vis-a-vis". Both examples in the comments are correct use, but they are both somewhat archaic or extra-formal, and "vis-a-vis" might be confused to imply that you talked to someone in-person or face-to-face if not used correctly.