I need someone to set me straight. Guitar output (non active pickups) is a line signal. Synth output is a line signal but at a higher level. Is this signal measured in ohms ? What is the measured difference between what is considered a mic level and a line level signal?

I may be wrong, but as I understand it:

Line Level = -10dBu
Mic Level = +4dBu

Instrument level is widely variable, but not considered "line level". I believe it can range up to around +24dBu. For example if you patch your guitar into a high gain stomp box on the way to the pre's instrument input, you will hit the instrument input much hotter than with the guitar alone..

The preceding message is an interpretation as understood by a drummer. YMMV

Not quite.
Normal guitar pickups are high impedance,
(hi-Z) they want to drive 500,000 ohms or so.
Line level will happily drive 10,000 ohms or less.
A guitar will not.

Cheap mics, and even the famous Shure Green Bullet,
are also high impedance. All decent mics are low
impedance.

So to feed a "line level" input, you need to
amplify the signal.

To convert a mic or guitar level signal
from high impedance to low, you can use a cheap
(or expensive if you are a gear slutz)
transformer.

And on a related note, I have a box that has a "instrument amp output" that I swear is marked -20dB, but I'll look at it to be sure.