Clutch?

So when engine is turned off I can put transmission into gear without pressing in the clutch, but when engine is on, I can not do that.

Is this normal

Yep.

Never did it before, odd. I thought the synchros were toast.

:)

You'll notice that if parked, it will often go into gear, but not always without pushing the clutch. If the cogs are matched up (or close) you can shift into gear; if not, it won't go and you'll get resistance.