Unless you have GPSS installed, your autopilot will not automatically re-join the airway. WIthout GPSS, you would dial in a reasonable intercept heading from your current position, fly until on the airway, then turn to the appropriate airway heading before re-engaging the autopilot. My STEC-20 will not capture an assigned routing unless it is within +/- 10 degrees of the desired heading. If off by more than that, it may eventually capture, but not after a lot of seasick scalloping. I don't have GPSS yet, so I don't know how well it copes with a large cross-track error and a large intercept angle.
When flying IFR, it's always good to have a sectional chart open (That's my default view on my EFB) so you can see the minimum safe altitude for the quadrant you are flying in. That way, if you are solid IMC making deviations, you at least know if you are safely above obstacles. ATC will normally help as well when you go off course for weather, but they are not PIC.
If you want to go direct to the next waypoint instead of re-joining the airway or previous routing, it's always a good idea to confirm with ATC. Often, ATC will beat you to that request and just offer a clearance direct if in radar contact and you are above MVA.