Applescript date manipulation to get multiple formats
set theMonth to do shell script " date -v2d -v1m -v99y +%B%n%b%n%m%n%-m"


-> "January

Jan

01

1"

set theDay to do shell script " date -v2d -v1m -v99y +%A%n%a%n%d%n%-d"


-> "Saturday

Sat

02

2"

set theYear to do shell script " date -v2d -v1m -v99y +%Y%n%y"


-> "1999

99"


-v  flag  adjusts the date item without changing the real date.
-v2d   is 2nd day
-v1m  is first month
-v99y  is the year 1999

The date formatters are:
%n  new line
%B  full month name
%b  abbr month name
%m   month number with leading zero
%-m   month number without leading zero


The other formatters follow the same way.  You can find more format info by simply googling.

If you want to do it all in applescript then I suggest you read through
MacScripter / Dates &amp; Times in AppleScripts

---------- update

I do think it is more efficient doing it with the shell script. But if I was going to try and do it in Applescript alone. I would use handlers to either pad or shorten the item. And the just pass the month, year and day to them to sort.

set {year:y, month:m, day:d} to current date
--set m to m + 1

set theYearLong to y as string
set theYearShort to shorten(y)


set theMonthNumberZero to pad((m as integer) as string)
set theMonthNumber to ((m as integer) as string)
set theMonthLong to m as string
set theMonthShort to shorten(m)


set theDayNumberZero to pad((d as integer) as string)
set theDayNumber to ((d as integer) as string)



on pad(thisNumber)
    if length of thisNumber = 1 then
        return "0" &amp; thisNumber
    else
        return thisNumber
    end if
end pad


on shorten(thisItem)

    if class of thisItem is integer then
        return characters 3 thru -1 of (thisItem as text) as string
    else
        return characters 1 thru 3 of (thisItem as text) as string
    end if
end shorten


There probably is a better way of doing it but this example may give you an idea..