It would depend on how you used the property.
"Don’t include any costs you can claim a tax deduction for, such as the cost of capital works." - reading [if there were rental income, then expenses that CAN be claimed in there would not be included in the cost base]
but not sure about the strata fees we have paid ?
Strata levies would need to be a bit more careful. The 'normal' strata fees you treat it like other expenses so would only be able to add strata levies that couldn't be claimed in the rental income. The 'special' strata levies you would need to be careful as it could be capital cost or asset instead of expense such as retification works or a new intercom.
for renovations where we don't have the original invoice - any suggestions on how we can include those costs?
If it's more recent, you could try to ask the whomever you paid for a copy of the invoice(s). I'm not sure if this would okay for ATO if you audited: use payment records [with communication or contract records]