The Scots host Belgium at Hampden on Friday in their Group A World Cup qualifier before playing in Skopje next Tuesday.
Strachan has added to his options following the withdrawal of West Brom midfield duo James Morrison and Graham Dorrans on Sunday and Hull City's George Boyd on Monday.
Derby's Craig Bryson, fellow midfielder Kevin Thomson of Hibernian, Birmingham winger Chris Burke and Rangers defender Lee Wallace have all been added to the pool.
Strachan's assistant Mark McGhee said: Scotland assistant McGhee added Hull player to that list.
He said: "George Boyd has gone home. He has had some sort of ankle injury I
"We know about James and Graham, they are a big loss, both of them, but we
brought in other and we are getting on with it. Quite a few of them didn't train on Monday but we are expecting a full complement on Tuesday."
Meanwhile, Hearts defender Jordan McGhee has been added to the Scotland U-21 squad for their UEFA European Under-21 Championship qualifying match against the Netherlands.