So as much as he ever has anything one might call a "strategy", here is what I think it is:
-declare a national emergency and say he is building his wall without Congressional approval
-various organizations go to court and are granted a stay on the building of the wall
-after a few weeks or months the Supreme Court renders a decision, probably in his favour since he does seem to have the power to do I
Meanwhile, his base is sated, the Republicans in Congress are divided even more, and the Democrats are united even more. Trump's odds of being re-elected, and the Republicans' odds of holding the Senate and taking back the House get longer, thanks to the above-mentioned divisions but more due to a steady flow of reporting on how silly and wasteful the whole thing is, and how other parts of government, the military in particular, are short of funds that have been diverted to building the wall.
I am thinking something similar:
1. Go on TV tonight and declare a National Emergency and say that he is going to build the Wall based on this declaration and using discretionary "National Emergency Funds" (whatever that means).
2. At the same time, excoriate the Democrats for the government shutdown and declare that he is willing to sign a bill from the House/Senate that re-opens the government without the need for appropriating money for the wall, since that will come from his "National Emergency Funds".
3. Take credit for re-opening the government when the House and Senate send him a bill tomorrow.
4. Various organizations go to court to fight on the Wall being built based on a National Emergency declaration. Court fight drags on and everyone forgets about it as we move on to the next crisis. In the meantime, continue to campaign about the need for the Wall.
5. It doesn't matter what happens. If he wins in court, great, he gets to build the Wall with National Emergency Funds. If he loses in court, then excoriate the courts, the media, the Democrats, etc...
It's the only way I can see him getting out of this mess that he created, and still declare himself the Victor.