Interesting. Here below are my comments.
1.)I made an application in the xx-year xxxx to xxxx, x, x years x to take on holiday. <I will be in December 22, 2008 to return to work.> (never use this sentence format, it is wrong and ugly) I <have to discuss> (wrong tense, wrong usage) with Chen OK, she has helped me deal with labor-related work. I <do not go out> (wrong tense) in the meantime, <Miss Chen on behalf of my daily business> (missing verb, imcomplete sentence), you can contact her. <If there are some special things can also be made to contact me.> (HK chinglish, wrong grammar) （中文原文：我特意申請在xxxx年x月x日至xxxx年x月x日放取大假。我會在2008年12月22日返回工作崗位。我已經與陳小姐商討好了，有勞她幫助我處理有關工作。在我不外出在其間，陳小姐代我處理日常事務，您們可以與她聯絡。倘若有一些特別事情，亦可致電與我聯絡。）
>> I have applied for X days of annual leave from <date> to <date> and I will resume duty on 22 Dec 08. I dicussed with Miss Chen and she agreed to take up my duties within the period, so you can call her for any business. If you have any urgent matters, you can conatct me at XXXX XXXX.
Use simple past tense instead of present perfect tense.
Remove the adverb, "directly". "call me at" is good enough.
You don't have to tell that you applied for the annual leave
To rewrite the sentence, I'll go like this:
I'll be on annual leave from xx December and be back to office on 22 Dec 88. During my absence, you may call Miss Chan for assistance. In case of urgency, you may call me at 9xxxxxxx
2.) <When I was a good thing to deal with> (I don't understand what were you talking about), <I will immediately return to work> (HK chinglish). （中文原文：當我處理好事情後，我馬上會返回工作崗位。）
>> When I have finished my personal business, I will go back to office immediately.
Grammar is OK but the tone is bad. It's like saying, "I will never go back to office unless I have finished my personal business."
I would say, "Sorry I'll have to attend some personal matter which is very urgent. I guess I'll be back at 10.00 a.m. (or on 20 Dec 2008)."
I'll try to give a best estimate such that your boss or colleague have an idea of my availability. They need to prioritise their tasks again in order to help me when I'm away from work.
3.) <I am in December 18, 2008 to December 19, 2008 to take sick leave for two days.> (never use this sentence format, it is wrong and ugly). Now, I feel <physical condition has improved some.> (HK chinglish, wrong grammar) I go to work immediately <to deal with affairs work .> (HK chinglish). （中文原文：我在2008年12月18日至2008年12月19日放取了兩天病假。現在，我感覺身體狀況已經轉好了一些。我立即上班，處理工作事務。）
> I took sick leaves on 18 and 19 Dec 08 but I went back to office immediately when I felt better.
Going back to office should be a past action.
"Now" is odd here, confusing the timing. We may take it out.
The term "現在" is not logical even when it is used in the original Chinese sentence.
4.) On 2008 Dec. 18, when I <get up> (wrong tense), I <feel> (wrong tense) <physically uncomfortable> (wrong usage, HK chinglish), clearly <can not deal with> (wrong tense),day-to-day affairs. I <call> (wrong tense) Miss Li, <informing> (wrong grammar) her that I <can not go> (wrong tense) to work. Since then, I <see> (wrong tense) a doctor. My doctor told me (sudden correct in this sentence!) suffering from a cold and asked me <one day of rest> (incomplete meaning). In order to <rehabilitation> (wrong grammar, wrong usage. You did not suffer from any physical or mental disability!) as soon as possible, I have decided to follow the advice of doctors <to stay> (stay what, incomplete sentence). （中文原文：在2008年12月18上，當我起床時，我感到自己身體不舒適，不能清醒地處理日常事務。我立即致電李小姐，通知她我不能上班工作。其後，我去看醫生。我的醫生告訴我患上感冒，並要求我休息一天。為了盡快康復，我決定遵從醫生吩咐。）
In the morning of 18 Dec 08 I told Ms Li on the phone that I was sick and could not get to work. Then, I saw a doctor. He told me that I got a flu and advised me to take an one-day sick leave. I took the doctor's advice for quicker recovery.
I think it is difficult to correct the sentence. Rewriting it is easier.
