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Two numbers in Japanese have two pronunciation alternatives.

  * 四 / 4 can be pronounced either "よん" (yon) or "し" (shi)
  * 七 / 7 can be pronounced either "しち" (shichi) or "なな" (nana)

I know that "し" (shi) can be avoided because it has the same pronunciation as
"死" which means "death" but how strong is the taboo and how does it relate to
factors such as formality and politeness when choosing which form to use? Is
it just a matter of superstition or should speakers be more sensitive?

"しち" (shichi) vs "なな" (nana) seems to be less discussed since it doesn't
involve taboo or superstition as far as I know but again what about formality
and politeness etc?
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word-choice pronunciation numbers readings
How to choose between "よん" (yon) vs "し" (shi) for "四" (4) and "しち" (shichi) vs "なな" (nana) for "七" (7)?
I don't know that there are any rules, per se. I just know that in certain
situations, you use one and not the other. Like ４月 is し・がつ, not よん・がつ, and
9:00 is く・じ, not きゅう・じ. I think it's just a matter of memorizing these
"irregularities".
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2011-06-01T15:03:48.907
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よん is a 訓読み(kunyomi) reading of 4 and し is a 音読み(onyomi). なな is a kunyomi
reading of 7 and しち is a onyomi.

To make a long story short kunyomi is a native Japanese pronunciation and
onyomi are pronunciation that were derived from classical Chinese.

In the case of numbers shi and shichi (onyomi) is used when you are counting
things. For example, ichi ni san shi go, ... It is also used in months, like
四月(shigatsu) and 七月(shichigatsu)

When you point out that you have 70 yen you say nana juu en. (In this case use
kunyomi) Kunyomi is typically used in cases where you point out you have X of
some item. Counting in kunyomi is very unnatural so you almost never hear
people say ichi ni san yon go, ... but it is used when you count backwards.

These are just basic rules, there is one exception I can think of and that is
people, sometimes you do hear 七人(shichi-nin) when you talk about people.
However, as far as I know, it is very unnatural for people to use shi and
shichi used when talking about large numbers in the 10's, 100's, etc so use
the kunyomi (yon and nana) for that.
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When you are counting, the reading "よん" is more used, because, as you also
reminded, "し" is too similar to "死" which means "death".  
Usually when a Kanji is "alone" you use the On reading, but in this case when
counting, you don't do that for 4 and 7.

To quote [this page](http://en.wikipedia.org/wiki/Japanese_numerals) here:

> In modern Japanese, _the digits are given the On'yomi readings_ **except 4
> and 7** , which are called yon and nana respectively. Alternate readings are
> used in month names, day-of-month names, and fixed phrases.

I want to highlight something else: With the number "4" there is an exception,
for example, when telling the time:

> 四時 the reading is "yoji" and not "*yonji".

or with the classifier つ:

> 四つ the reading is "yotsu" and not "*yontsu".

I can't recall exceptions regarding the number 7, but if I come up with
something, I'll make sure to add it.
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There is also a strong geographical, if not toponymic, component: at the
anecdotal level, I have noticed that Kansai/Kyoto people are more likely to
read 四 as し and 七 as しち (in newly encountered words), when Tokyo people will
tend to opt for よん and なな.

A most famous example would be the streets of Kyoto:

Kyoto is laid out in a grid pattern (or a shogi board, to be exact) with East-
West streets numbered from 1 to 10 (starting from the North): 一条, 二条, 三条 etc.

If you ask out-of-town (Japanese) visitors to read aloud the name for 四条 and
七条, they'll have little idea how to go at it. When pressed, they will probably
opt for よんじょう and ななじょう (particularly the latter), when it is in fact しじょう and
しちじょう.
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