Can you run 240v and 120v in the same conduit?

Yes  it can be done.  And it is permissable in the NEC  use THHN, or THWN wire and allow for derating of the conductor size since you  have 5+ current carrying conductors in the conduit. The length of the run and the load  will determine  what wire size you need.  Safest method is have a qualified professional electrician do the work.

Do you have two separate 240 feeds into you house and you’re running a single 240 off of one and two 120s off of the other? Even if you did, you want a sub panel. You’re going to run a single 240 line to your sub panel. From there, you’ll get two 120 circuits but your welder, lights and outlets will all be on the same circuit from your house. The only way around it is to have a second service installed 

The volts is not what is important, because it all ready established. What is important is the current or the "load". The load establishes the size of wire and more is added because of the length of run. The panel and incoming wires must be large enough to handle the added load. Unless you want to take a community ed course on electricity you should hire a electrician. Grampa B

as long as you use THHN or better insulated wire/cable, you should be fine. internet search will find something on this -- it depends on conduit size. be sure to check your wire size for the length of run -- if memory serves, 50 feet means next larger than normal size.

I tend to use two lengths of 10/3 or 12/3 UG cable for this ... putting the two 110v circuits in as red and black in one cable.

You can put the cables all in the same conduit. You will have to determine what size conduit. At least 2" if it is a straight run. It might be easier to put each cable in its on conduit. 3/4" and 1". Putting multiple cables in a single conduit is hard to do. It gets stiff and bent and wedges up. The sub panel is easier and you would have future space for more circuits in the shed as you expand over the years.  Next year you will be thinking air conditioner, then a beer cooler, electric grill, air compressor, winter heater, etc.  You might also want to run a water line in your ditch.  Bath room. UF cable.  

you can run them in the same conduit, plenty of room in a 1” pipe