Throughput is simple: assuming the client is saturating the network, the server only needs to count the received bytes, and divide that by some duration.
This post explains this topic in a greater detail.
Iperf 2 calculates Jitter for UDP only. It is based on what is prescribed within by RTP implementation, as stated by the code.
RTP is used in implementations of audio streaming, where jitter plays a major role, so it's a good place to take the algorithm from - what Iperf reports is what many applications where you would be interested in jitter would see.
See RFC 1889, section 6.3.1, "interarrival jitter" field:
The interarrival jitter J is defined to be the mean deviation (smoothed
absolute value) of the difference D in packet spacing at the receiver compared
to the sender for a pair of packets. As shown in the equation below, this is
equivalent to the difference in the "relative transit time" for the two
packets; the relative transit time is the difference between a packet's RTP
timestamp and the receiver's clock at the time of arrival, measured in the same
units.
If Si is the RTP timestamp from packet i, and Ri is the time of arrival in RTP
timestamp units for packet i, then for two packets i and j, D may be expressed
as
D(i,j)=(Rj-Ri)-(Sj-Si)=(Rj-Sj)-(Ri-Si)
The interarrival jitter is calculated continuously as each data packet i is
received from source SSRC_n, using this difference D for that packet and the
previous packet i-1 in order of arrival (not necessarily in sequence),
according to the formula
J=J+(|D(i-1,i)|-J)/16