This is not really an answer (the only possible answer gave doncherry in the comments: It seems, that you do not have properly installed the
asymptote style files). But it will be too long for a comment, so read this one here:
I want strongly discourage you to follow the instructions of the wiki linked by you: It is a very bad idea to put additional packages into the MiKTeX root trees, cf. Purpose of local texmf trees. Instead you should use the official opportunity to create an own (local) TeXMF tree.
For that do the following:
Start MiKTeX portable by execution of the included
Do a right mouse click on the traybar icon, that appeared and choose “MiKTeX Options”.
Choose there the tab “Roots” and add your local TEXMF tree. It will be saved as relative path in the
<miktex-portable>\miktex\config\miktexstartup.ini. Your local TEXMF tree must not be a subfolder of
<miktex-portable>. Last click on “OK” for saving changes.
Your local TeXMF tree must, as doncherry already mentioned, be TDS compliant. Let’s say you’ve created a folder
X: as your current removable drive) then create the subfolder tree
X:\localtexmf\tex\latex\asymptote\ and copy all
sty files from the original Asymptote folder into the subfolder
Now the important part, that you seem to have forgotten: Open again the “MiKTeX Options”. On tab “General” you have to update the file name database: click on “Refresh FNDB”.
Just for convenience I suggest also to add an own start batch script:
First make an save copy of the original
miktex-portable.cmd. Then open this file with a text editor and change it in the following way:
Change the path to the
Asymptote executables according to your settings (don’t delete the part
%MOBILDRIVE%\). Then you can (and should!) use the command line prompt, that you get with right click on the traybar icon. (Hint: type there
echo %path% – the beginning should read similar to
See also Using Asymptote with MiKTeX, though this is not adapted to portable use.
This is in parts a copy of myself: Setting TEXMFHOME variable when using Miktex portable.