I'm going to go for a scan spree by gutting my ship and installing the 5 best scanners.

I want to know, how much boosting can I add, theoretically id like to add the following;

Subspace seeker +175
Tachyon cylinder +50
Continuum Beacon +15% scan
Stryll seeker +10% scan

So I think a quick calculation of 5x scanners would be 1130 (base best)
+ 175 = 1305
+ 50 = 1355
+ 15% = 1558
+ 10% = 1713

Can you use this many items at once to boost and is there logic to the amplification?

Any advice would be fantastic

everything applied to your ship comes into effect in the order that you use it. (so if you used the artifacts in that order, that is the scan power you will get) And remember, you can't use the same artifact more than one at a time (for example, you cant use a subspace seeker if you already have one active).

But since theyre all of different names you believe you can use them all in a burst?!

Yes, you can stack all 4. The static bonus ones are easy enough. Not sure exactly how % stacks, but I've always thought it was (1+bonus%+bonus%) for example 10% and 20% turns out to be additive: 130% of the static number.

Also note:
- A rare mission (protogrid entry followup) gives 5x buffs of +20% scan
- Explorer profession gives +20% scan

As I said before, ship bonuses work in the order that you use them. so 10% and 20% actually go:
100%*110%*120%= 132%

Also, additive bonuses do the same. So a tachyon cylinder and subspace seeker give different bonuses depending on if you use them before or after the % bonuses. (however I don't know if effects like the explorer profession work before or after)
Examples using base 1000 scan, with continuum beacon (+15%), stryll seeker (+10%), subspace seeker (+175), and tachyon cylinder (+50):
percent then additive: 1000*1.1*1.2+175+50= 1545 scan
additive then percent: 1000+175+50*1.1*1.2= 1617 scan

I got to 1948 scan with everything installed and using the protogrid buff.

I found a great deal of crap...20 minutes of 99% chance of finding things and I get not so hot results, was disappointing.