Can I use a wire rope to support strings of lights?
Practical Advice

Let's consider the solution to a more difficult application: hanging a fabric shade sail. The static load is higher due to the weight of the fabric and the wind load is higher due to the sail effect. Furthermore, when a company publishes instructions for hanging this shade they have a strong interest in making sure it doesn't rip off your house. So if you follow their advice for you application you have applied a strong margin of safety.

For a 12' sail the linked instructions specify a 1/8" thick galvanized steel 4" x 4" post mounted 10 degrees from vertical or a 5" x 5" timber post mounted 20 degrees from vertical. Either post to be mounted in a concrete footing measuring 15.5" square and 31" deep. If you anchor the primary wire into the ground you could further stiffen this setup.

For the house anchors they recommend steel supports between the fascia and the rafter/truss. I suspect this is overkill for the four secondary anchors but may be advised for the primary wire if you want it to be rather taut. As @isherwood suggested mock it up and tug hard on the primary wire to get a sense of the forces involved.

Way more then you want or need to consider

Force on a deflected wire

First consider Why Can't a Rope be Pulled Completely Straight. Each wire end will exert a transverse force F_tw = mg / (2 sin &#x03B8;) where m is a single mass at the center of the wire, g is the acceleration due to gravity (9.8 m/s/s), and &#x03B8; is the angle of deflection. If you are willing to accept a 12" deflection of the primary wire then F_tw ~ 50 N/kg * m = 16.7 ft * m.

For m on the primary wire use the total mass of the supported wires and lights as well as the primary wire itself.

Dynamic loads

Besides the static load of the wires and lights you have to consider transverse wind and ice loads. Utility companies do this when sizing poles (pdf). In the coldest climates they plan for 4 lbs/sq ft wind load on a wire radius that has increased by 0.5" due to sleet and ice accumulation. In warmer climates there's no increase to the wire radius but the wind load planned is 9 lbs/sq ft.

When doing these calculations it is customary to ignore the bracing effect of the other wires. So when computing the wind load on the primary wire we would ignore the fact that the light wires will resist the wind blowing away from the house.

For your configuration I would consider two orthogonal loads. The primary support wire can push right-to-left. The other wires can pull in-and-out of your figure. In each case add up the sq ft of wire and lights and multiply to calculate a wind load. Your support beam will need to support this load at the anchor point near it's top. Your other anchor points will need to support some fraction of these loads as well.

Force on a cantilevered beam

You need a beam that can support the resulting transverse wire and transverse wind load. It also needs to support it's own vertical weight but this is not normally an issue. Your question doesn't specify the height but the deflection of the pole grows linearly with the height of the mount point. Assuming the pole can handle the loads it must be securely anchored into the ground like a fence post.

Building anchors

The wires need to be anchored to the building. For highest strength you should anchor to the fascia (not the soffit) at a point close to the rafters. Don't forget that these anchor points have to carry the very same loads as the post. There are four secondary anchor points splitting the load from the lights and one primary anchor point which carries the same load as the post.

Safety Factors

When planning an installation it's important to apply safety factors. Overload capacity factors for utility poles are included in the link above and they range from 1.0 to 2.5. The strength of the pole or anchor points are also derated by a factor as low as 0.65. These are values applied by knowledgeable engineers. For a DIY project I would replace brains with brawn and build it at least twice as strong.