measuring load cell output by a oscilloscope
Millivolts, yes - nanovolts, no. If you have a scope with 1 mV/div sensitivity, using x1 probes you might read ~100 NV fairly reliably, although noise pickup will be a problem.

A third alternative is to build your own x100 amplifier and use that with your existing meter. Something like this - although in this case it's a x101 amplifier.







simulate this circuit &ndash; Schematic created using CircuitLab

Note that you'll need a pretty good amplifier, with very low input offset voltage. Depending on what is used, it may be necessary to include an offset adjustment pot which you use to zero out errors just before you make a measurement. It's a tradeoff of convenience vs cost: cheaper (roll your own) vs easier to use (buy a good one). Your choice.