1.8uV is even lower than MCP 2.8 uV p-p (typical). is this noise multiplied by gain.
Yes, or more precisely, multiplied by the
noise gain (which is simply the feedback ratio). There's an Analog appnote on it, you should search for.
Also I compared TL071 which claims low noise, to TI LM358. 18 for TL071 to 40 for LM358 is not much of a difference. Let's say you want to amplify audio signal of 16kHz. That's 18*4 = 72 for TL071 to 40*4=160 nV which is only about twice as big.
1. You should include units to make these calculations harder to get wrong;
2. You didn't take the sqrt correctly.

(3. "Amplify an audio signal of 16kHz" doesn't necessarily mean the total bandwidth is 16kHz exactly. It can be less. Or will probably be more in a practical case!)
Writing it out,
18nV/rtHz * sqrt(16000Hz) = 18nV/rtHz * 126.49 rtHz = 2276 nV *
rtHz/rtHz = 2.3 uV.
Rather than taking the sqrt again, the noise for the other amp is simply the ratio,
2.3 uV * (40 / 18)
( (nV/rtHz) / (nV/rtHz) ) = 5.1 uV.
Still not much, for many purposes (it's plenty stable for a control loop, say, and comparable to the noise from a similarly cheap voltage reference), but you could go for a gain as high as 100 in such a stage (because the fT is ~low MHz), bringing the output noise to nearly a millivolt (for the LM358 case). Needless to say, this would make a poor phonograph preamplifier!

The JFET amp isn't bad, but its relatively high noise, and extremely low current noise, strongly suggests it for high impedance applications (megohms!). In that case, its noise factor can be quite good indeed.
But even without a high impedance source, it definitely outperforms LM358.

There are better of both kinds, of course. The takeaway is to match the amp's input impedance (in terms of noise impedance e_n / i_n) to the source, at least broadly (within a factor of 2 for NF < 3dB, I think?).
About the input current noise - it's effect on the output depends on resistance connected to inputs - gain resistors, signal output impedance, etc, right?
Yes. And for DC bias reasons, you want the Thevenin equivalent DC resistance, at each input pin, to be equal. (For some amps, you want the AC resistance to be matched as well: LT1028's input current noise is somewhat correlated between the two pins, so you cancel out the correlated noise by using equal AC resistances.)
Tim