Actually, I think you are talking about 'usage' rather than 'tone'.

In English, when we talk about 'tone', it refers to their sound of our voice, the tome of our voice.

'usage' means 'identifying and using the right word at the right time (in a certain situation).

For example:

'thank you is more formal than 'thanks'.

So we use 'thanks' when we are speaking to our friends and we use 'thank you' when we are speaking to someone older or to someone that has a higher position than us.

One way to see and learn words that have a similar meaning and may be used in different situations is to check a Thesaurus.

Here is a good link:

http://www.thesaurus.com/

Native English speakers usually learn which words to use in certain situations by reading which words are in used in different situations. So, it may be helpful to read example sentences when you are looking at the words in the thesaurus or in a dictionary, and also in anything written in English.

Hope my comment are helpful...

- Will you send me ～ ?
[this is informal / it is a form of a request / used with someone you know or at the same lvel as you]

- Would you send me ～ ?
[this is a little formal and polite / a form of a request / used with anyone]

- Could you send me ～ ?
[informal / request / used with anyone / asking if it is possible (could?) / used with people at the same level]

- I'd appreciate it if you could send me ～.
[a little formal and respectful / showing your gratitude / used with friends or superiors]

- It would be appreciated if you could send me ～.
[formal / but not personal because of the use of 'it' rather than the personal 'I or we would appreciate it if ... / not used very often, i.e., not necessary to be expressed this way]

- I'd appreciate your sending me ～.
[between formal and informal / showing your gratitude / between a request and an order / used with equals and superiors with whom you have a good working relationship]

NOTE: Tone, formality and informality are not clearly defined terms, so different people will have different opinions about what constitutes (what is) tone, therefore, others may not agree with my explanations, although I feel reasonably confident that my explanations are based on practices in Canada and the US.

My suggestion is: when in doubt, stick to the simplest, shortest, plainest, most literal choice.

In your list of examples, the two shortest are "Please send me" and "Kindly send me." "Please" is part of beginner's vocabulary, "kindly" is not. 

It's true that "send me" is shorter than "please send me." However, a beginner should recognize that "send me" is a <em>command</em> and not a <em>request</em> and therefore isn't polite.

With respect to politeness, the important thing is to include <em>anything</em> that signals politeness. The details really don't matter. "It's the thought that counts." For example, if you send a thank-you note, what matters is the <em>fact</em> that you sent a thank-you note, not what words you used. 

When in doubt, err in the direction of formality. <em>Do not be afraid to use the English you are taught in the classroom</em>. It is <em>possible</em> for English to be so excessively formal that it is out of place or makes a negative impression. English teachers do <em>not</em> teach overly formal English. You will <em>not</em> offend anyone by saying "If I were you" instead of "if I was you." 

People will simply speak of your "charming accent" and it is almost a saying that "foreign speakers speak better English than we do."

(It is possible to imagine situations in which a <em>native</em> speaker could give offense by using correct classroom English. For example, if one conspicuously used a formal phrase immediately after someone else used an informal equivalent, so that it sounded like a correction, or by using in way that signals "I am educated and you are not.")

Helen

Your question about "If I were.." and "If I was" relates to the Mood of the verb and not the Tense of the verb. "If I were" is called the Subjunctive Mood.

MOOD

Mood shows the attitude of the speaker or the writer to the action or state described by the verb.

Declarative / Indicative Mood
The Declarative or Indicative Mood is the normal form of a verb used in ordinary statements and questions, in contrast with the Imperative and the Subjunctive.

e.g. She went home.
e.g. Has she called yet?

Imperative Mood
Imperatives are verbs used to give orders, commands and instructions. The form used is usually the same as the Base Form. It is one of the three moods of an English Verb. Imperatives should be used carefully in English; to give firm orders or commands, but not as much when trying to be polite or show respect to the other person.
e.g. Give me that tape, please.
e.g. Go home.
e.g. Come and see me.

Subjunctive Mood
The subjunctive is the Mood of a Verb, used to express doubts or show hopes, doubts, wishes, etc..
It is not used very much in modern English surviving in a few expressions such as 'If I were you' in the 2nd Conditional and expressions like 'God save the Queen', ‘Be that as it may’, and 'so be it'.

The Subjunctive mood is explained well in the following website:

http://www.quickanddirtytips.com/education/grammar/subjunctive-verbs

Elanvital
I now understand what you meant by 'tone'.
The website link describes it well.
Tone does refer to formal and informal ways of saying or writing things.
The tone you use depends on the relationship you have with the person you are addressing.
I will try to explain the usage (when to use) and tone in the examples you provided:

- Send me an application form by airmail.
[This is informal / it is a command or order / used with friends or someone you work with who is at the same level as you]

- Please send me ～.
[This is between informal and formal / it is a request, not an order or command / used with friends or strangers]

- Kindly send me ～.
[This is extremely formal and respectful / it is a very diplomatic request / used with people at a higher level than you / the word 'please' is just as good as 'kindly']

- You are kind enough to send me ～.
[This is not a proper sentence / do not use]

- I would be obliged if you would send me ～.
[extremely formal / it means that you would owe the sender a favour in the future if they do this favour for you / we don't use this very often]