Can SteerMouse sensitivity be automated?
You should check if SteerMouse supports applescript by opening applescript editor and then clicking File -> Open Dictionary. If it does, please reply back.

In the meantime, there is a indirect solution, which is to have two separate preferences files for work and home and switching between them.

First, set your home settings. You'll find the preferences file at ~/Library/Preferences/SteerMouse.prefs. Copy that and rename the copy to SteerMouse_home.prefs. Then adjust them for work and copy those preferences and name them SteerMouse_work.prefs. 

Then, in applescript editor, copy this code and save it as an application.

property myLocation : ""

if myLocation is "" then
    set myLocation to "Home"
end if

if myLocation is "Home" then
    do shell script "mv -f ~/Library/Preferences/SteerMouse_home.prefs ~/Library/Preferences/SteerMouse.prefs"
    set myLocation to "Work"

else if myLocation is "Work" then
    do shell script "mv -f ~/Library/Preferences/SteerMouse_work.prefs ~/Library/Preferences/SteerMouse.prefs"
    set myLocation to "Home"
end if

#You'll only need this part if the app needs to be restarted for the changes to occur.
tell application "SteerMouse"
    quit
    activate
end tell