How can there be undecidable languages in P/1?
if $L\in P/poly$ then there is a machine that decides any input $x$,  given the advice $a_{|x|}$. 

However, if the advice is not given, maybe no machine can decide $L$. This is what happens in the unary case. Note that the machine doesn't know the advice and cannot compute it, i.e.,  the set of advices (for a specific $L$) may be an undecidable language. 

On the other hand, if someone gives you this (possibly undecidable) set, you have more power at hands. Similarly, if you can compute this set (for a certain $L$), say get $a_n$ in $f(n)$ time, then $L$ clearly belongs to $DTIME(poly(f(n)))$.